Module 9: Limit Cycles (cont.)

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    "html": "\n\n<img alt=\"Content Folder\" src=\"/images/ci/sets/set01/folder_on.gif\" class=\"item_icon\">\n\n<div class=\"item clearfix\" id=\"_7048791_1\">\n\n <h3 id=\"anonymous_element_9\">\n  <span class=\"reorder editmode hideme\"><span><img src=\"/images/ci/icons/generic_updown.gif\" alt=\"\"></span></span>\n\n\n            <a href=\"/webapps/blackboard/content/listContent.jsp?course_id=_194578_1&amp;content_id=_7048791_1\"><span style=\"color:#0067AC;\">Lectures and Related Content</span></a>\n      </h3><a href=\"#\" class=\"ally-alternative-formats ally-prominent-af-download-button\" data-ally-external-id=\"content:_7048791_1\" data-ally-upload-type=\"RichContent\" title=\"Alternative formats\" style=\"display: none\">\n    <span class=\"ally-sr-only\">\n  \n\n\n            Lectures and Related Content\n      </span>\n</a>\n\n   \n </div>\n\n\n\n<div class=\"details\">\n    <div class=\"vtbegenerated\"> \n <p>Please click the folder link above to access the Module 9 instructional content. Module 9 contains the following:</p> \n <ul> \n  <li>09A:&nbsp; Relaxation Oscillators</li> \n  <li>09B:&nbsp;Weakly nonlinear Oscillators</li> \n  <li>09C:&nbsp;Two Time Scales</li> \n </ul> \n</div>\n  </div>\n\n <div id=\"_7048791_1previewModule\" class=\"moduleSample\">\n </div>\n",
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        "body": "\n    <div> \n <p>Please click the folder link above to access the Module 9 instructional content. Module 9 contains the following:</p> \n <ul> \n  <li>09A:&nbsp; Relaxation Oscillators</li> \n  <li>09B:&nbsp;Weakly nonlinear Oscillators</li> \n  <li>09C:&nbsp;Two Time Scales</li> \n </ul> \n</div>\n  "
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        "html": "\n\n<img alt=\"Item\" src=\"/images/ci/sets/set01/document_on.gif\" class=\"item_icon\">\n\n<div class=\"item clearfix\" id=\"_7048790_1\">\n\n <h3 id=\"anonymous_element_8\">\n  <span class=\"reorder editmode hideme\"><span><img src=\"/images/ci/icons/generic_updown.gif\" alt=\"\"></span></span>\n\n\n\n     <span style=\"color:#0067ac;\">Module at a Glance</span>\n </h3><a href=\"#\" class=\"ally-alternative-formats ally-prominent-af-download-button\" data-ally-external-id=\"content:_7048790_1\" data-ally-upload-type=\"RichContent\" title=\"Alternative formats\" style=\"display: none\">\n    <span class=\"ally-sr-only\">\n  \n\n\n\n     Module at a Glance\n </span>\n</a>\n\n   \n </div>\n\n\n\n<div class=\"details\">\n    <div class=\"vtbegenerated\"> \n <p>In this module we'll determine the shape and periodic behavior of the closed orbit of a two-dimensional system.</p> \n <p><strong><span style=\"font-size: small; color: #0067ac;\">Objectives</span></strong></p> \n <ul> \n  <li>Determine the behavior of a relaxation operator.</li> \n  <li>Analyze the dynamics of a weakly nonlinear oscillator when small perturbations are applied to a linear oscillator.</li> \n  <li>Examine the various time scales that arise from weakly nonlinear oscillators.</li> \n  <li>Apply the model of a child on a swing to discover effective ways to use a swing near a fixed point.</li> \n </ul> \n <p><span style=\"color: #0067ac;\"><strong><span style=\"font-size: small;\">How to complete this module:</span></strong></span></p> \n <ol> \n  <li>Watch the video lectures 9A through 9F.&nbsp;</li> \n  <li>Complete the reading assignment.</li> \n  <li>Respond to the discussion board question.</li> \n  <li>Complete the assignment.</li> \n </ol> \n</div>\n  </div>\n\n <div id=\"_7048790_1previewModule\" class=\"moduleSample\">\n </div>\n",
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    "html": "\n\n<img alt=\"Item\" src=\"/images/ci/sets/set01/document_on.gif\" class=\"item_icon\">\n\n<div class=\"item clearfix\" id=\"_7048790_1\">\n\n <h3 id=\"anonymous_element_8\">\n  <span class=\"reorder editmode hideme\"><span><img src=\"/images/ci/icons/generic_updown.gif\" alt=\"\"></span></span>\n\n\n\n     <span style=\"color:#0067ac;\">Module at a Glance</span>\n </h3><a href=\"#\" class=\"ally-alternative-formats ally-prominent-af-download-button\" data-ally-external-id=\"content:_7048790_1\" data-ally-upload-type=\"RichContent\" title=\"Alternative formats\" style=\"display: none\">\n    <span class=\"ally-sr-only\">\n  \n\n\n\n     Module at a Glance\n </span>\n</a>\n\n   \n </div>\n\n\n\n<div class=\"details\">\n    <div class=\"vtbegenerated\"> \n <p>In this module we'll determine the shape and periodic behavior of the closed orbit of a two-dimensional system.</p> \n <p><strong><span style=\"font-size: small; color: #0067ac;\">Objectives</span></strong></p> \n <ul> \n  <li>Determine the behavior of a relaxation operator.</li> \n  <li>Analyze the dynamics of a weakly nonlinear oscillator when small perturbations are applied to a linear oscillator.</li> \n  <li>Examine the various time scales that arise from weakly nonlinear oscillators.</li> \n  <li>Apply the model of a child on a swing to discover effective ways to use a swing near a fixed point.</li> \n </ul> \n <p><span style=\"color: #0067ac;\"><strong><span style=\"font-size: small;\">How to complete this module:</span></strong></span></p> \n <ol> \n  <li>Watch the video lectures 9A through 9F.&nbsp;</li> \n  <li>Complete the reading assignment.</li> \n  <li>Respond to the discussion board question.</li> \n  <li>Complete the assignment.</li> \n </ol> \n</div>\n  </div>\n\n <div id=\"_7048790_1previewModule\" class=\"moduleSample\">\n </div>\n",
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        "body": "\n    <div> \n <p>In this module we'll determine the shape and periodic behavior of the closed orbit of a two-dimensional system.</p> \n <p><strong><span>Objectives</span></strong></p> \n <ul> \n  <li>Determine the behavior of a relaxation operator.</li> \n  <li>Analyze the dynamics of a weakly nonlinear oscillator when small perturbations are applied to a linear oscillator.</li> \n  <li>Examine the various time scales that arise from weakly nonlinear oscillators.</li> \n  <li>Apply the model of a child on a swing to discover effective ways to use a swing near a fixed point.</li> \n </ul> \n <p><span><strong><span>How to complete this module:</span></strong></span></p> \n <ol> \n  <li>Watch the video lectures 9A through 9F.&nbsp;</li> \n  <li>Complete the reading assignment.</li> \n  <li>Respond to the discussion board question.</li> \n  <li>Complete the assignment.</li> \n </ol> \n</div>\n  "
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        "html": "\n\n<img alt=\"Tools Area\" src=\"/webapps/ATLS-AresCourseReserves-bb_bb60/images/ares.gif\" class=\"item_icon\">\n\n<div class=\"item clearfix\" id=\"_7048792_1\">\n\n <h3 id=\"anonymous_element_10\">\n  <span class=\"reorder editmode hideme\"><span><img src=\"/images/ci/icons/generic_updown.gif\" alt=\"\"></span></span>\n\n\n            <a href=\"/webapps/blackboard/content/launchLink.jsp?course_id=_194578_1&amp;content_id=_7048792_1&amp;mode=view\"><span style=\"color:#0067AC;\">Readings</span></a>\n      </h3><a href=\"#\" class=\"ally-alternative-formats ally-prominent-af-download-button\" data-ally-external-id=\"content:_7048792_1\" data-ally-upload-type=\"RichContent\" title=\"Alternative formats\" style=\"display: none\">\n    <span class=\"ally-sr-only\">\n  \n\n\n            Readings\n      </span>\n</a>\n\n   \n </div>\n\n\n\n<div class=\"details\">\n    <div class=\"vtbegenerated\"> \n <p><span style=\"font-size: 13px;\">This week's reading assignment includes the following:</span></p> \n <ul> \n  <li><span data-contrast=\"auto\" xml:lang=\"EN-US\">Strogatz, Steven H</span><span data-contrast=\"auto\" xml:lang=\"EN-US\">.&nbsp;</span><em><span data-contrast=\"none\" xml:lang=\"EN-US\">Nonlinear Dynamics and Chaos with Student Solutions Manual: With Applications to Physics, Biology, Chemistry, and Engineering</span></em><span data-contrast=\"auto\" xml:lang=\"EN-US\">.&nbsp;</span><span data-contrast=\"auto\" xml:lang=\"EN-US\">CRC Press, 2018.</span><span data-ccp-props=\"{&quot;134233279&quot;:true,&quot;469777462&quot;:[360],&quot;469777927&quot;:[0],&quot;469777928&quot;:[1]}\">&nbsp;</span> \n   <ul> \n    <li><span data-contrast=\"auto\" xml:lang=\"EN-US\">Chapter 7</span><span data-contrast=\"auto\" xml:lang=\"EN-US\">&nbsp;(pp. 213-229)</span></li> \n   </ul> </li> \n </ul> \n</div>\n  </div>\n\n <div id=\"_7048792_1previewModule\" class=\"moduleSample\">\n </div>\n",
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    "html": "\n\n<img alt=\"Tools Area\" src=\"/webapps/ATLS-AresCourseReserves-bb_bb60/images/ares.gif\" class=\"item_icon\">\n\n<div class=\"item clearfix\" id=\"_7048792_1\">\n\n <h3 id=\"anonymous_element_10\">\n  <span class=\"reorder editmode hideme\"><span><img src=\"/images/ci/icons/generic_updown.gif\" alt=\"\"></span></span>\n\n\n            <a href=\"/webapps/blackboard/content/launchLink.jsp?course_id=_194578_1&amp;content_id=_7048792_1&amp;mode=view\"><span style=\"color:#0067AC;\">Readings</span></a>\n      </h3><a href=\"#\" class=\"ally-alternative-formats ally-prominent-af-download-button\" data-ally-external-id=\"content:_7048792_1\" data-ally-upload-type=\"RichContent\" title=\"Alternative formats\" style=\"display: none\">\n    <span class=\"ally-sr-only\">\n  \n\n\n            Readings\n      </span>\n</a>\n\n   \n </div>\n\n\n\n<div class=\"details\">\n    <div class=\"vtbegenerated\"> \n <p><span style=\"font-size: 13px;\">This week's reading assignment includes the following:</span></p> \n <ul> \n  <li><span data-contrast=\"auto\" xml:lang=\"EN-US\">Strogatz, Steven H</span><span data-contrast=\"auto\" xml:lang=\"EN-US\">.&nbsp;</span><em><span data-contrast=\"none\" xml:lang=\"EN-US\">Nonlinear Dynamics and Chaos with Student Solutions Manual: With Applications to Physics, Biology, Chemistry, and Engineering</span></em><span data-contrast=\"auto\" xml:lang=\"EN-US\">.&nbsp;</span><span data-contrast=\"auto\" xml:lang=\"EN-US\">CRC Press, 2018.</span><span data-ccp-props=\"{&quot;134233279&quot;:true,&quot;469777462&quot;:[360],&quot;469777927&quot;:[0],&quot;469777928&quot;:[1]}\">&nbsp;</span> \n   <ul> \n    <li><span data-contrast=\"auto\" xml:lang=\"EN-US\">Chapter 7</span><span data-contrast=\"auto\" xml:lang=\"EN-US\">&nbsp;(pp. 213-229)</span></li> \n   </ul> </li> \n </ul> \n</div>\n  </div>\n\n <div id=\"_7048792_1previewModule\" class=\"moduleSample\">\n </div>\n",
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        "title": "Readings",
        "body": "\n    <div> \n <p><span>This week's reading assignment includes the following:</span></p> \n <ul> \n  <li><span data-contrast=\"auto\" xml:lang=\"EN-US\">Strogatz, Steven H</span><span data-contrast=\"auto\" xml:lang=\"EN-US\">.&nbsp;</span><em><span data-contrast=\"none\" xml:lang=\"EN-US\">Nonlinear Dynamics and Chaos with Student Solutions Manual: With Applications to Physics, Biology, Chemistry, and Engineering</span></em><span data-contrast=\"auto\" xml:lang=\"EN-US\">.&nbsp;</span><span data-contrast=\"auto\" xml:lang=\"EN-US\">CRC Press, 2018.</span><span data-ccp-props=\"{&quot;134233279&quot;:true,&quot;469777462&quot;:[360],&quot;469777927&quot;:[0],&quot;469777928&quot;:[1]}\">&nbsp;</span> \n   <ul> \n    <li><span data-contrast=\"auto\" xml:lang=\"EN-US\">Chapter 7</span><span data-contrast=\"auto\" xml:lang=\"EN-US\">&nbsp;(pp. 213-229)</span></li> \n   </ul> </li> \n </ul> \n</div>\n  "
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overflow: hidden;\"> \n  <div style=\"float: left; clear: left;\"> \n   <div style=\"float: left; clear: both;\"> \n    <iframe width=\"320\" height=\"240\" style=\"width: 604px; height: 386px;\" frameborder=\"0\" scrolling=\"no\" allowfullscreen=\"true\" allow=\"autoplay *; fullscreen *; encrypted-media *; camera *; microphone *;\" src=\"/webapps/osv-kaltura-bb_bb60/content/iframe.jsp?url=..%2FLtiMashupPlayIframeWrapperResponsive%3FplayUrl%3D%2Fbrowseandembed%2Findex%2Fmedia%2Fentryid%2F0_b5dw8u01%2FshowDescription%2Ffalse%2FshowTitle%2Ffalse%2FshowTags%2Ffalse%2FshowDuration%2Ffalse%2FshowOwner%2Ffalse%2FshowUploadDate%2Ffalse%2FplayerSize%2F400x285%2FplayerSkin%2F30749451%2F&amp;thumbnail=https://cdnsecakmi.kaltura.com/p/1458241/sp/145824100/thumbnail/entry_id/0_b5dw8u01/version/0&amp;title=Game+of+Cat+and+Mouse+-+Numberphile&amp;course_id=_194578_1&amp;content_id=_7048793_1\"></iframe> \n   </div> \n  </div> \n  <div id=\"container_0.9708790138064458\" class=\"hide-icon hidden\" style=\"margin-top: 30px; float: left; clear: left;\"> \n   <div style=\"float: left; clear: left; margin-right: 8px;\"> \n    <div style=\"float: left; clear: both;\"> \n     <a class=\"lb\" style=\"text-decoration: none; color: #333333;\" href=\"../LtiMashupPlayIframeWrapperResponsive?playUrl=/browseandembed/index/media/entryid/0_b5dw8u01/showDescription/false/showTitle/false/showTags/false/showDuration/false/showOwner/false/showUploadDate/false/playerSize/400x285/playerSkin/30749451/&amp;course_id=_194578_1\" target=\"_blank\" title=\"Game of Cat and Mouse - Numberphile\"> <img border=\"0\" src=\"https://cdnsecakmi.kaltura.com/p/1458241/sp/145824100/thumbnail/entry_id/0_b5dw8u01/version/0\"> </a> \n    </div> \n    <div style=\"float: left; clear: both; width: 100%; background: url('/images/ci/ng/rumble_button_back.gif') 50% 50%; padding-top: 2px; padding-bottom: 2px; text-decoration: none; color: #333333; text-align: center;\"> \n     <a class=\"lb\" style=\"text-decoration: none; color: #333333;\" href=\"../LtiMashupPlayIframeWrapperResponsive?playUrl=/browseandembed/index/media/entryid/0_b5dw8u01/showDescription/false/showTitle/false/showTags/false/showDuration/false/showOwner/false/showUploadDate/false/playerSize/400x285/playerSkin/30749451/&amp;course_id=_194578_1\" target=\"_blank\" title=\"Game of Cat and Mouse - Numberphile\"> Watch Media </a> \n    </div> \n   </div> \n   <div style=\"float: left; clear: right;\"> \n    <table style=\"margin: 0px !important; border-collapse: collapse;\"> \n     <tbody> \n      <tr style=\"vertical-align: top;\"> \n       <td style=\"padding: 0px !important;\"><b>Name:</b></td> \n       <td style=\"padding: 0px 0px 0px 20px !important;\"><b>Game of Cat and Mouse - Numberphile</b></td> \n      </tr> \n      <tr style=\"vertical-align: top;\"> \n       <td style=\"padding: 0px !important;\">Duration:</td> \n       <td style=\"padding: 0px 0px 0px 20px !important;\">&nbsp;</td> \n      </tr> \n      <tr style=\"vertical-align: top;\"> \n       <td style=\"padding: 0px !important;\">Added:</td> \n       <td style=\"padding: 0px 0px 0px 20px !important;\">12 Aug 2019 08:00 AM</td> \n      </tr> \n      <tr style=\"vertical-align: top;\"> \n       <td style=\"padding: 0px !important;\">Added By:</td> \n       <td style=\"padding: 0px 0px 0px 20px !important;\">DIANE BANNER</td> \n      </tr> \n      <tr style=\"vertical-align: top;\"> \n       <td style=\"padding: 0px !important;\">Description:</td> \n       <td style=\"padding: 0px 0px 0px 20px !important;\">&nbsp;</td> \n      </tr> \n      <tr style=\"vertical-align: top;\"> \n       <td style=\"padding: 0px !important;\">Tags:</td> \n       <td style=\"padding: 0px 0px 0px 20px !important;\">625.781, stein</td> \n      </tr> \n     </tbody> \n    </table> \n   </div> \n  </div> \n </div> \n <p>Write down differential equations for both problems (7.1.9 and the video). Discuss the dynamics of both problems. Describe if a limit cycle is present or what the presence of a limit cycle would indicate.&nbsp;</p> \n <p>You may access the discussion forum by selecting the link above or by going to the discussion area from the left menu bar.</p> \n <p><br></p> \n <div style=\"font-family: 'Open Sans', sans-serif; text-shadow: none !important; letter-spacing: normal !important;\"> \n  <strong style=\"font-family: inherit; text-shadow: none !important; letter-spacing: normal !important; margin: 0px; padding: 0px; border: 0px; outline: 0px; font-weight: bold; font-style: inherit; font-size: 13px;\"><span data-contrast=\"auto\" xml:lang=\"EN-US\" style=\"font-family: inherit; text-shadow: none !important; letter-spacing: normal !important; margin: 0px; padding: 0px; border: 0px; outline: 0px; font-weight: inherit; font-style: inherit; font-size: 13px;\"></span></strong> \n </div> \n <p><strong style=\"font-family: 'Open Sans', sans-serif; text-shadow: none !important; letter-spacing: normal; margin: 0px; padding: 0px; border: 0px; outline: 0px; font-weight: bold; font-style: normal; font-size: 13px; color: #000000; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: #ffffff; text-decoration-style: initial; text-decoration-color: initial;\">Due: Sunday 11:59 pm</strong></p> \n <p style=\"font-family: inherit; text-shadow: none !important; letter-spacing: normal !important; margin: 0px 0px 1em; padding: 0px; border: 0px; outline: 0px; font-weight: inherit; font-style: inherit; font-size: 13px;\"></p> \n <p><br></p> \n <p><br></p> \n</div>\n  </div>\n\n <div id=\"_7048793_1previewModule\" class=\"moduleSample\">\n </div>\n",
        "url": "https://blackboard.jhu.edu/webapps/blackboard/content/launchLink.jsp?course_id=_194578_1&content_id=_7048793_1&mode=view",
        "title": "Module 9 Discussion"
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    "html": "\n\n<img alt=\"Discussion Board\" src=\"/images/ci/sets/set01/discussion_on.gif\" class=\"item_icon\">\n\n<div class=\"item clearfix\" id=\"_7048793_1\">\n\n <h3 id=\"anonymous_element_11\">\n  <span class=\"reorder editmode hideme\"><span><img src=\"/images/ci/icons/generic_updown.gif\" alt=\"\"></span></span>\n\n\n            <a href=\"/webapps/blackboard/content/launchLink.jsp?course_id=_194578_1&amp;content_id=_7048793_1&amp;mode=view\"><span style=\"color:#0067ac;\">Module 9 Discussion</span></a>\n      </h3><a href=\"#\" class=\"ally-alternative-formats ally-prominent-af-download-button\" data-ally-external-id=\"content:_7048793_1\" data-ally-upload-type=\"RichContent\" title=\"Alternative formats\" style=\"display: none\">\n    <span class=\"ally-sr-only\">\n  \n\n\n            Module 9 Discussion\n      </span>\n</a>\n\n   \n </div>\n\n\n\n<div class=\"details\">\n    <div class=\"vtbegenerated\"> \n <p>Watch this video and read problem 7.1.9 in the Strogatz textbook – a similar problem but different dynamics.&nbsp;</p> \n <div style=\"width: 604px; overflow: hidden;\"> \n  <div style=\"float: left; clear: left;\"> \n   <div style=\"float: left; clear: both;\"> \n    <iframe width=\"320\" height=\"240\" style=\"width: 604px; height: 386px;\" frameborder=\"0\" scrolling=\"no\" allowfullscreen=\"true\" allow=\"autoplay *; fullscreen *; encrypted-media *; camera *; microphone *;\" src=\"/webapps/osv-kaltura-bb_bb60/content/iframe.jsp?url=..%2FLtiMashupPlayIframeWrapperResponsive%3FplayUrl%3D%2Fbrowseandembed%2Findex%2Fmedia%2Fentryid%2F0_b5dw8u01%2FshowDescription%2Ffalse%2FshowTitle%2Ffalse%2FshowTags%2Ffalse%2FshowDuration%2Ffalse%2FshowOwner%2Ffalse%2FshowUploadDate%2Ffalse%2FplayerSize%2F400x285%2FplayerSkin%2F30749451%2F&amp;thumbnail=https://cdnsecakmi.kaltura.com/p/1458241/sp/145824100/thumbnail/entry_id/0_b5dw8u01/version/0&amp;title=Game+of+Cat+and+Mouse+-+Numberphile&amp;course_id=_194578_1&amp;content_id=_7048793_1\"></iframe> \n   </div> \n  </div> \n  <div id=\"container_0.9708790138064458\" class=\"hide-icon hidden\" style=\"margin-top: 30px; float: left; clear: left;\"> \n   <div style=\"float: left; clear: left; margin-right: 8px;\"> \n    <div style=\"float: left; clear: both;\"> \n     <a class=\"lb\" style=\"text-decoration: none; color: #333333;\" href=\"../LtiMashupPlayIframeWrapperResponsive?playUrl=/browseandembed/index/media/entryid/0_b5dw8u01/showDescription/false/showTitle/false/showTags/false/showDuration/false/showOwner/false/showUploadDate/false/playerSize/400x285/playerSkin/30749451/&amp;course_id=_194578_1\" target=\"_blank\" title=\"Game of Cat and Mouse - Numberphile\"> <img border=\"0\" src=\"https://cdnsecakmi.kaltura.com/p/1458241/sp/145824100/thumbnail/entry_id/0_b5dw8u01/version/0\"> </a> \n    </div> \n    <div style=\"float: left; clear: both; width: 100%; background: url('/images/ci/ng/rumble_button_back.gif') 50% 50%; padding-top: 2px; padding-bottom: 2px; text-decoration: none; color: #333333; text-align: center;\"> \n     <a class=\"lb\" style=\"text-decoration: none; color: #333333;\" href=\"../LtiMashupPlayIframeWrapperResponsive?playUrl=/browseandembed/index/media/entryid/0_b5dw8u01/showDescription/false/showTitle/false/showTags/false/showDuration/false/showOwner/false/showUploadDate/false/playerSize/400x285/playerSkin/30749451/&amp;course_id=_194578_1\" target=\"_blank\" title=\"Game of Cat and Mouse - Numberphile\"> Watch Media </a> \n    </div> \n   </div> \n   <div style=\"float: left; clear: right;\"> \n    <table style=\"margin: 0px !important; border-collapse: collapse;\"> \n     <tbody> \n      <tr style=\"vertical-align: top;\"> \n       <td style=\"padding: 0px !important;\"><b>Name:</b></td> \n       <td style=\"padding: 0px 0px 0px 20px !important;\"><b>Game of Cat and Mouse - Numberphile</b></td> \n      </tr> \n      <tr style=\"vertical-align: top;\"> \n       <td style=\"padding: 0px !important;\">Duration:</td> \n       <td style=\"padding: 0px 0px 0px 20px !important;\">&nbsp;</td> \n      </tr> \n      <tr style=\"vertical-align: top;\"> \n       <td style=\"padding: 0px !important;\">Added:</td> \n       <td style=\"padding: 0px 0px 0px 20px !important;\">12 Aug 2019 08:00 AM</td> \n      </tr> \n      <tr style=\"vertical-align: top;\"> \n       <td style=\"padding: 0px !important;\">Added By:</td> \n       <td style=\"padding: 0px 0px 0px 20px !important;\">DIANE BANNER</td> \n      </tr> \n      <tr style=\"vertical-align: top;\"> \n       <td style=\"padding: 0px !important;\">Description:</td> \n       <td style=\"padding: 0px 0px 0px 20px !important;\">&nbsp;</td> \n      </tr> \n      <tr style=\"vertical-align: top;\"> \n       <td style=\"padding: 0px !important;\">Tags:</td> \n       <td style=\"padding: 0px 0px 0px 20px !important;\">625.781, stein</td> \n      </tr> \n     </tbody> \n    </table> \n   </div> \n  </div> \n </div> \n <p>Write down differential equations for both problems (7.1.9 and the video). Discuss the dynamics of both problems. Describe if a limit cycle is present or what the presence of a limit cycle would indicate.&nbsp;</p> \n <p>You may access the discussion forum by selecting the link above or by going to the discussion area from the left menu bar.</p> \n <p><br></p> \n <div style=\"font-family: 'Open Sans', sans-serif; text-shadow: none !important; letter-spacing: normal !important;\"> \n  <strong style=\"font-family: inherit; text-shadow: none !important; letter-spacing: normal !important; margin: 0px; padding: 0px; border: 0px; outline: 0px; font-weight: bold; font-style: inherit; font-size: 13px;\"><span data-contrast=\"auto\" xml:lang=\"EN-US\" style=\"font-family: inherit; text-shadow: none !important; letter-spacing: normal !important; margin: 0px; padding: 0px; border: 0px; outline: 0px; font-weight: inherit; font-style: inherit; font-size: 13px;\"></span></strong> \n </div> \n <p><strong style=\"font-family: 'Open Sans', sans-serif; text-shadow: none !important; letter-spacing: normal; margin: 0px; padding: 0px; border: 0px; outline: 0px; font-weight: bold; font-style: normal; font-size: 13px; color: #000000; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: #ffffff; text-decoration-style: initial; text-decoration-color: initial;\">Due: Sunday 11:59 pm</strong></p> \n <p style=\"font-family: inherit; text-shadow: none !important; letter-spacing: normal !important; margin: 0px 0px 1em; padding: 0px; border: 0px; outline: 0px; font-weight: inherit; font-style: inherit; font-size: 13px;\"></p> \n <p><br></p> \n <p><br></p> \n</div>\n  </div>\n\n <div id=\"_7048793_1previewModule\" class=\"moduleSample\">\n </div>\n",
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        "title": "Module 9 Discussion",
        "body": "\n    <div> \n <p>Watch this video and read problem 7.1.9 in the Strogatz textbook – a similar problem but different dynamics.&nbsp;</p> \n <div> \n  <div> \n   <div> \n     \n   </div> \n  </div> \n  <div id=\"container_0.9708790138064458\"> \n   <div> \n    <div> \n     <a href=\"../LtiMashupPlayIframeWrapperResponsive?playUrl=/browseandembed/index/media/entryid/0_b5dw8u01/showDescription/false/showTitle/false/showTags/false/showDuration/false/showOwner/false/showUploadDate/false/playerSize/400x285/playerSkin/30749451/&amp;course_id=_194578_1\" target=\"_blank\" title=\"Game of Cat and Mouse - Numberphile\">  </a> \n    </div> \n    <div> \n     <a href=\"../LtiMashupPlayIframeWrapperResponsive?playUrl=/browseandembed/index/media/entryid/0_b5dw8u01/showDescription/false/showTitle/false/showTags/false/showDuration/false/showOwner/false/showUploadDate/false/playerSize/400x285/playerSkin/30749451/&amp;course_id=_194578_1\" target=\"_blank\" title=\"Game of Cat and Mouse - Numberphile\"> Watch Media </a> \n    </div> \n   </div> \n   <div> \n    <table> \n     <tbody> \n      <tr> \n       <td><b>Name:</b></td> \n       <td><b>Game of Cat and Mouse - Numberphile</b></td> \n      </tr> \n      <tr> \n       <td>Duration:</td> \n       <td>&nbsp;</td> \n      </tr> \n      <tr> \n       <td>Added:</td> \n       <td>12 Aug 2019 08:00 AM</td> \n      </tr> \n      <tr> \n       <td>Added By:</td> \n       <td>DIANE BANNER</td> \n      </tr> \n      <tr> \n       <td>Description:</td> \n       <td>&nbsp;</td> \n      </tr> \n      <tr> \n       <td>Tags:</td> \n       <td>625.781, stein</td> \n      </tr> \n     </tbody> \n    </table> \n   </div> \n  </div> \n </div> \n <p>Write down differential equations for both problems (7.1.9 and the video). Discuss the dynamics of both problems. Describe if a limit cycle is present or what the presence of a limit cycle would indicate.&nbsp;</p> \n <p>You may access the discussion forum by selecting the link above or by going to the discussion area from the left menu bar.</p> \n  \n <div> \n   \n </div> \n <p><strong>Due: Sunday 11:59 pm</strong></p> \n  \n  \n  \n</div>\n  "
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        "html": "\n\n<img alt=\"Assignment\" src=\"/images/ci/sets/set01/assignment_on.gif\" class=\"item_icon\">\n\n<div class=\"item clearfix\" id=\"_7048794_1\">\n\n <h3 id=\"anonymous_element_12\">\n  <span class=\"reorder editmode hideme\"><span><img src=\"/images/ci/icons/generic_updown.gif\" alt=\"\"></span></span>\n\n\n            <a href=\"/webapps/assignment/uploadAssignment?content_id=_7048794_1&amp;course_id=_194578_1&amp;group_id=&amp;mode=view\"><span style=\"color:#0067ac;\">Module 9 Assignment</span></a>\n      </h3><a href=\"#\" class=\"ally-alternative-formats ally-prominent-af-download-button\" data-ally-external-id=\"content:_7048794_1\" data-ally-upload-type=\"RichContent\" title=\"Alternative formats\" style=\"display: none\">\n    <span class=\"ally-sr-only\">\n  \n\n\n            Module 9 Assignment\n      </span>\n</a>\n\n   \n </div>\n\n\n\n<div class=\"details\">\n    <div class=\"vtbegenerated\"> \n <ul> \n  <li>Complete the following problems from chapter 7 of the Strogatz textbook: <strong>7.1.3</strong> (3 pts.);&nbsp;<strong>7.2.1</strong> (3pts.); <strong>7.3.1</strong> (12 pts.);&nbsp;<strong>7.5.3</strong> (4 pts.); <strong>7.5.5</strong> (4 pts.);&nbsp;<strong>7.6.2</strong> (10 pts.)</li> \n  <li>Upload your work in PDF format by selecting the link above.</li> \n </ul> \n <p style=\"margin-left: 30px;\"></p> \n <div style=\"font-family: 'Open Sans', sans-serif; text-shadow: none !important; letter-spacing: normal !important;\"> \n  <strong style=\"font-family: inherit; text-shadow: none !important; letter-spacing: normal !important; margin: 0px; padding: 0px; border: 0px; outline: 0px; font-weight: bold; font-style: inherit; font-size: 13px;\"><span data-contrast=\"auto\" xml:lang=\"EN-US\" style=\"font-family: inherit; text-shadow: none !important; letter-spacing: normal !important; margin: 0px; padding: 0px; border: 0px; outline: 0px; font-weight: inherit; font-style: inherit; font-size: 13px;\"></span></strong> \n </div> \n <p><strong style=\"font-family: 'Open Sans', sans-serif; text-shadow: none !important; letter-spacing: normal; margin: 0px; padding: 0px; border: 0px; outline: 0px; font-weight: bold; font-style: normal; font-size: 13px; color: #000000; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: #ffffff; text-decoration-style: initial; text-decoration-color: initial;\">Due: Tuesday 11:59&nbsp;pm</strong></p> \n <p style=\"font-family: inherit; text-shadow: none !important; letter-spacing: normal !important; margin: 0px 0px 1em; padding: 0px; border: 0px; outline: 0px; font-weight: inherit; font-style: inherit; font-size: 13px;\"></p> \n</div>\n  </div>\n\n <div id=\"_7048794_1previewModule\" class=\"moduleSample\">\n </div>\n",
        "url": "https://blackboard.jhu.edu/webapps/assignment/uploadAssignment?content_id=_7048794_1&course_id=_194578_1&group_id=&mode=view",
        "title": "Module 9 Assignment"
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    "html": "\n\n<img alt=\"Assignment\" src=\"/images/ci/sets/set01/assignment_on.gif\" class=\"item_icon\">\n\n<div class=\"item clearfix\" id=\"_7048794_1\">\n\n <h3 id=\"anonymous_element_12\">\n  <span class=\"reorder editmode hideme\"><span><img src=\"/images/ci/icons/generic_updown.gif\" alt=\"\"></span></span>\n\n\n            <a href=\"/webapps/assignment/uploadAssignment?content_id=_7048794_1&amp;course_id=_194578_1&amp;group_id=&amp;mode=view\"><span style=\"color:#0067ac;\">Module 9 Assignment</span></a>\n      </h3><a href=\"#\" class=\"ally-alternative-formats ally-prominent-af-download-button\" data-ally-external-id=\"content:_7048794_1\" data-ally-upload-type=\"RichContent\" title=\"Alternative formats\" style=\"display: none\">\n    <span class=\"ally-sr-only\">\n  \n\n\n            Module 9 Assignment\n      </span>\n</a>\n\n   \n </div>\n\n\n\n<div class=\"details\">\n    <div class=\"vtbegenerated\"> \n <ul> \n  <li>Complete the following problems from chapter 7 of the Strogatz textbook: <strong>7.1.3</strong> (3 pts.);&nbsp;<strong>7.2.1</strong> (3pts.); <strong>7.3.1</strong> (12 pts.);&nbsp;<strong>7.5.3</strong> (4 pts.); <strong>7.5.5</strong> (4 pts.);&nbsp;<strong>7.6.2</strong> (10 pts.)</li> \n  <li>Upload your work in PDF format by selecting the link above.</li> \n </ul> \n <p style=\"margin-left: 30px;\"></p> \n <div style=\"font-family: 'Open Sans', sans-serif; text-shadow: none !important; letter-spacing: normal !important;\"> \n  <strong style=\"font-family: inherit; text-shadow: none !important; letter-spacing: normal !important; margin: 0px; padding: 0px; border: 0px; outline: 0px; font-weight: bold; font-style: inherit; font-size: 13px;\"><span data-contrast=\"auto\" xml:lang=\"EN-US\" style=\"font-family: inherit; text-shadow: none !important; letter-spacing: normal !important; margin: 0px; padding: 0px; border: 0px; outline: 0px; font-weight: inherit; font-style: inherit; font-size: 13px;\"></span></strong> \n </div> \n <p><strong style=\"font-family: 'Open Sans', sans-serif; text-shadow: none !important; letter-spacing: normal; margin: 0px; padding: 0px; border: 0px; outline: 0px; font-weight: bold; font-style: normal; font-size: 13px; color: #000000; font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: #ffffff; text-decoration-style: initial; text-decoration-color: initial;\">Due: Tuesday 11:59&nbsp;pm</strong></p> \n <p style=\"font-family: inherit; text-shadow: none !important; letter-spacing: normal !important; margin: 0px 0px 1em; padding: 0px; border: 0px; outline: 0px; font-weight: inherit; font-style: inherit; font-size: 13px;\"></p> \n</div>\n  </div>\n\n <div id=\"_7048794_1previewModule\" class=\"moduleSample\">\n </div>\n",
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        "title": "Module 9 Assignment",
        "body": "\n    <div> \n <ul> \n  <li>Complete the following problems from chapter 7 of the Strogatz textbook: <strong>7.1.3</strong> (3 pts.);&nbsp;<strong>7.2.1</strong> (3pts.); <strong>7.3.1</strong> (12 pts.);&nbsp;<strong>7.5.3</strong> (4 pts.); <strong>7.5.5</strong> (4 pts.);&nbsp;<strong>7.6.2</strong> (10 pts.)</li> \n  <li>Upload your work in PDF format by selecting the link above.</li> \n </ul> \n  \n <div> \n   \n </div> \n <p><strong>Due: Tuesday 11:59&nbsp;pm</strong></p> \n  \n</div>\n  "
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