The oscillations of a swinging pendulum can be simulated with the following nonlinear model: where ? =
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The oscillations of a swinging pendulum can be simulated with the following nonlinear model:
where ? = the angle of displacement, g = the gravitational constant, and I = pendulum length. For small angular displacements, the sin ? is approximately equal to ? and the model can be linearized as
Use ode45 to solve for ? as a function of time for both the linear and nonlinear models, where I = 0.6 m and g = 9.81 m/s 2 . First, solve for the case where the initial condition is for a small displacement (? = ?/8 and d? = 0). Then repeat the calculation for a large displacement (? = ?/2). For each case, plot the linear and nonlinear simulations on the same plot.
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