You wish to design a pendulum which moves a mass along an arc of length 40 cm when the angle with the vertical changes by 20 degrees. What should be the length L in meters of the pendulum? Enter the numerical answer without units. Your answer must be within 5% of the exact answer to receive credit.

The length of the pendulum cord is approximately 114.592 centimeters.

Explanation:

We include a representation of the motion of the pendulum in the image attached below. The trajectory described by the pendulum is represented by the following geometrical expression:

(1)

Where:

- Angular change with the vertical, measured in radians.

- Length of the pendulum cord, measured in centimeters.

- Arc, measured in centimeters.

If we know that and , then the length of the pendulum cord is.

The length of the pendulum cord is approximately 114.592 centimeters.