The figure shows a pendulum with length L and the angle
Chapter 17, Problem 17.202(choose chapter or problem)
The figure shows a pendulum with length L and the angle from the vertical to the pendulum. It can be shown that , as a function of time, satisfies the nonlinear differential equation where is the acceleration due to gravity. For small values of we can use the linear approximation and then the differential equation becomes linear. (a) Find the equation of motion of a pendulum with length 1 m if is initially 0.2 rad and the initial angular velocity is . (b) What is the maximum angle from the vertical? (c) What is the period of the pendulum (that is, the time to complete one back-and-forth swing)? (d) When will the pendulum first be vertical? (e) What is the angular velocity when the pendulum is vertical?
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