Question

A simple pendulum is made from a 0.614-m-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?

Answer 1

Time period of a pendulum is given by:

T = 2*pi*sqrt (L/g)

L = 0.614 m

g = 9.81 m/sec^2

So

T = 2*pi*sqrt (0.614/9.81)

T = 1.57 sec

Now when ball was released from rest through a small angle, it's greatest speed will be when it passes through the point where pendulum is vertical.

Since after one T pendulum will return to its initial position, which means after T/4 it will be at vertical position, then after another T/4 it will be at other end of the motion, after another T/4 again it will return to the vertical point and finally after another T/4 it will return to it's initial position

which means pendulum will be at greatest speed after T/4 time

time elapsed = T/t = 1.57/4 = 0.393 sec

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