A simple pendulum is made from a 0.65m long string and a small ball attached to its free end. The ball is pulled to one side through a small angle and then released from rest. After the ball is released, how much time elapses before it attains its greatest speed?

Question

I am not sure how to solve this problem. I do have the formula, but it doesn't help: 2pi(f)= sqrt(g/L)

Thanks for your help!

Answer 1

An oscillating pendulum, or anything else in nature that involves "simple harmonic" (sinusoidal) motion, spends 1/4 of its period going from zero speed to maximum speed, and another 1/4 going from maximum speed to zero speed again, etc. After four quarter-periods it is back where it started. In your case the period is 1/f = 2 pi sqrt (L/g) = 1.62 s
One-quarter of that is 0.405 s
That is the answer.

Answer 2

How did you get 1.62 s?

Answer 3

Nevermind, I got it. Thank you!