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math245labprob04

# math245labprob04 - θ vs t measure the period of the...

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Math245 Simulation Problem #4, Fall 2008 Consider a nonlinear pendulum equation given by d 2 θ dt 2 + sin θ = 0 , with the initial condition θ = θ 0 and θ 0 = 0 at t = 0. 1. Simulate the system for seven different initial values θ 0 = { 0 . 1 , 0 . 5 , 1 , 1 . 5 , 2 , 2 . 5 , 3 } for 0 t 50, and plot their phase portrait ( θ 0 vs θ ) in one single figure. 2. By plotting the solution curve (
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Unformatted text preview: θ vs t ), measure the period of the oscillation for each initial values given above. Plot the period T as a function of initial value θ . Material to be submitted: 1. Printout of the phase portrait. 2. A Graph of T vs θ . Hand-writing graph is also acceptable....
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