
pendulum
A simple pendulum is made from a 0.673 mlong 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?

Well, we know that pendulums have their greatest speed when they are at maximum kinetic energy, and that is when the pendulum is straight up and down, and reaching that point the FIRST time is one fourth the time it would take for the pendulum to complete one full cycle.
We know that the period of the pendulum is represented by:
$\displaystyle T = 2\pi\sqrt{\frac{L}{g}}$
$\displaystyle \frac{1}{4}$ of this would be the time it takes to attain it's greatest speed:
$\displaystyle T = \frac{\pi}{2}\sqrt{\frac{L}{g}}$
Now we fill in all the details:
$\displaystyle T = \frac{\pi}{2}\sqrt{\frac{0.673}{9.81}}$
If you work it all out, you should get:
$\displaystyle T = 0.41 s$