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September 22, 2014

September 22, 2014

Posted by **Angel** on Wednesday, November 30, 2011 at 4:18pm.

A pendulum of length L is caused to swing by releasing it at an initial angle theta0 from the vertical. Because of air drag and friction in the mounting, the pendulum will eventually stop swinging. The equation of motion for the pendulum is given by the equation

In this relation, represents the angle of the pendulum with respect to vertical at any time t, is a damping coefficient, g is gravitational acceleration, and L is the length of the pendulum.

We want to study the effect of the damping coefficient, which models the effect of friction on the pendulum motion. Create plots of versus t for three different values of the damping coefficient. Put all three plots on the same graph. Choose values of that give distinctly different behaviors. (You will need to experiment to do this.) Use values of 0 = 10º and L = 2 ft. Note that must have units of inverse time for the equation to be dimensionally consistent.

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