A pendulum of mass 5.0 kg hangs in equilibrium. A frustrated student walks up to it and kicks the bob with a horizontal force of 30.0 . The force is applied over 0.3 seconds. How long does the pendulum have to be to have a period of 5.0 seconds? What is the maximum angle of displacement of the swinging pendulum?

The length is and the angle is

Explanation:

The period of the pendulum is related to its length by

where is the acceleration due to gravity.

Solving for we get

putting in and we get:

There are two forces acting on the pendulum: The gravitational force and the student's force. Therefore, the angular displacement that these forces give is

putting in , , and we get

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