Speed of a Pendulum

A simple pendulum is a mass at the end of a light string. If the length of the string is 1.4 m and the mass is released from rest at a point where the string makes an angle of 20 degrees with the vertical, what is the maximum speed of the pendulum?

Try energy conservation here:

U_i + K_i = U_f + K_f

i represents the initial position, where the mass is released from. f is the final position, at the bottom of the path. The zero level for potential energy is the bottom of the path.

The initial kinetic energy is zero, and the final potential energy is zero. So:

mgh = ½ mv_f², where h is the height from which the ball is released.

The m's cancel, leaving:

v_f = (2gh)^½

h can be determined from geometry. If L is the length of the string:

h = L - Lcos(θ) = L [1-cos(θ)]

With L = 1.40 m and θ = 20 degrees, h = 0.0844 m.

This gives v_f = (2gh)^½ = 1.29 m/s