Demonstration: Bungee Jumping - Revision history

HelmutKnaust at 04:16, 15 October 2013

2013-10-15T04:16:07Z

HelmutKnaust at 04:15, 15 October 2013

2013-10-15T04:15:43Z

HelmutKnaust at 17:08, 4 October 2013

2013-10-04T17:08:36Z

HelmutKnaust at 17:07, 4 October 2013

2013-10-04T17:07:54Z

HelmutKnaust at 17:07, 4 October 2013

2013-10-04T17:07:13Z

HelmutKnaust at 17:04, 4 October 2013

2013-10-04T17:04:48Z

HelmutKnaust at 17:15, 1 September 2013

2013-09-01T17:15:02Z

HelmutKnaust at 17:12, 1 September 2013

2013-09-01T17:12:38Z

HelmutKnaust at 17:00, 1 September 2013

2013-09-01T17:00:53Z

HelmutKnaust at 19:14, 31 August 2013

2013-08-31T19:14:03Z

← Older revision		Revision as of 04:16, 15 October 2013
Line 1:		Line 1:
	[[image:bungee_photo.jpg\|777px]]		[[image:bungee_photo.jpg\|777px]]
		+
		+

	<html><script type="text/javascript" src="http://www.wolfram.com/cdf-player/plugin/v2.1/cdfplugin.js"></script>		<html><script type="text/javascript" src="http://www.wolfram.com/cdf-player/plugin/v2.1/cdfplugin.js"></script>

@@ Line 1: / Line 1: @@
-[[image:bungee_photo.jpg|650px]]
+[[image:bungee_photo.jpg|777px]]
-−
-−
-−
-The following second order non-linear differential equation models a bungee jump:
-−
-:<math>m y''(t) + m g + b(y(t)) + \beta y'(t) = 0.</math>
-−
-Here y(t) denotes the position of the jumper at time t;  m is the mass of the jumper,  g is the gravitational constant, and <math>\beta</math> is the damping coefficient due to air resistance.
-−
-A bungee cord acts like a spring when stretched, but it has no restoring force when "compressed". The restoring force of the bungee cord b(y)  is thus modeled as follows:
-−
-:<math>b(y)=\left\{\begin{array}{cc}k y,&\mbox{ if }
-y\leq 0\\0, & \mbox{ if } y>0\end{array}\right.,</math>
-with <math>k</math> being the spring constant of the bungee cord.
-−
-−
-−
-The graph below shows the position y(t) and the acceleration <math>y''(t)</math> of the jumper at time t. The dashed line shows the equilibrium solution, i.e. the position of the jumper at the end of the jump. The natural length of the bungee cord is 100 ft, and the jump starts at a height of 100 ft.
-−
-You can change the weight w of the jumper, the damping coefficient <math>\beta</math>, and the spring constant k of the bungee cord.
-−
 <html><script type="text/javascript" src="http://www.wolfram.com/cdf-player/plugin/v2.1/cdfplugin.js"></script>
 <script type="text/javascript">
 var cdf = new cdfplugin();
-cdf.setDefaultContent('<a href="http://www.wolfram.com/cdf-player/"><img  src="bungee.png"></a>');
+cdf.embed('http://helmut.knaust.info/NB/Bungee.cdf', 777, 1200);
-cdf.embed('http://helmut.knaust.info/Demos/bungee.cdf', 694, 628);
 </script></html>

@@ Line 26: / Line 26: @@
 var cdf = new cdfplugin();
 cdf.setDefaultContent('<a href="http://www.wolfram.com/cdf-player/"><img  src="bungee.png"></a>');
-cdf.embed('http://helmut.knaust.info/Demos/bungee.cdf', 694, 588);
+cdf.embed('http://helmut.knaust.info/Demos/bungee.cdf', 694, 628);
 </script></html>

@@ Line 26: / Line 26: @@
 var cdf = new cdfplugin();
 cdf.setDefaultContent('<a href="http://www.wolfram.com/cdf-player/"><img  src="bungee.png"></a>');
-cdf.embed('http:/helmut.knaust.info/Demos/bungee.cdf', 694, 588);
+cdf.embed('http://helmut.knaust.info/Demos/bungee.cdf', 694, 588);
 </script></html>

@@ Line 26: / Line 26: @@
 var cdf = new cdfplugin();
 cdf.setDefaultContent('<a href="http://www.wolfram.com/cdf-player/"><img  src="bungee.png"></a>');
-cdf.embed('bungee.cdf', 694, 588);
+cdf.embed('http:/helmut.knaust.info/Demos/bungee.cdf', 694, 588);
 </script></html>

← Older revision		Revision as of 17:12, 1 September 2013
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	:<math>b(y)=\left\{\begin{array}{cc}k y,&\mbox{ if }		:<math>b(y)=\left\{\begin{array}{cc}k y,&\mbox{ if }
−	y\leq 0\\0, & \mbox{ if } y>0\end{array}\right.</math>, with k being the spring constant of the bungee cord.	+	y\leq 0\\0, & \mbox{ if } y>0\end{array}\right.,</math>
		+	with k being the spring constant of the bungee cord.

← Older revision		Revision as of 17:00, 1 September 2013
Line 16:		Line 16:


−	The ~~animation~~ below shows the position y(t) and the acceleration <math>y''(t)</math> of the jumper at time t. The dashed line shows the equilibrium solution, i.e. the position of the jumper at the end of the jump. The natural length of the bungee cord is 100 ft, and the jump starts at a height of 100 ft.	+	The graph below shows the position y(t) and the acceleration <math>y''(t)</math> of the jumper at time t. The dashed line shows the equilibrium solution, i.e. the position of the jumper at the end of the jump. The natural length of the bungee cord is 100 ft, and the jump starts at a height of 100 ft.

	You can change the weight w of the jumper, the damping coefficient <math>\beta</math>, and the spring constant k of the bungee cord.		You can change the weight w of the jumper, the damping coefficient <math>\beta</math>, and the spring constant k of the bungee cord.