Demonstration: Bungee Jumping

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-[[image:bungee_photo.jpg|600px]]
+[[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 k being the spring constant of the bungee cord.
-The animation below shows the position y(t) and the acceleration <math>y''(t)</math> of the jumper at time t.
-The natural length of the bungee cord is 100 ft, and the jump starts at a height of 100 ft. The dashed line shows the equilibrium solution, i.e. the position of the jumper at the end of the jump.
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-cdf.embed('http://helmut.knaust.info/Demos/bungee.cdf', 692, 536);
+cdf.embed('http://helmut.knaust.info/NB/Bungee.cdf', 777, 1200);
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Latest revision as of 22:16, 14 October 2013