pendulum as a timer

Using the Pendulum as a Timer

When using the pendulum to time a cart down a ramp, we set up some sort of obstacle for the cart to run into at the other end of its path. Then we release the pendulum at the same instant as the cart.

The pendulum will pass successively through the positions illustrated in the figure below.

If the pendulum passes through its equilibrium point (the point at which it naturally hangs, between the two supports, indicated by * marks in above figure) at the same instant the cart strikes the obstacle, then the pendulum will have gone through one, three, five, seven, ..., quarter cycles.

From release to equilibrium is one quarter-cycle, then from equilibrium to extreme position and back is another two quarter-cycles for a total of three, then from equilibrium to extreme position and back is another two quarter-cycles for a total five, etc..

Since the period of the pendulum is 2 `pi `sqrt(L / g), where L is its length and g the acceleration of gravity, we can easily determine the length of a quarter-cycle.

It will be necessary to adjust the length of the pendulum carefully and precisely in order to synchronize the cart's arrival at the obstacle with the arrival of the pendulum at its equilibrium position after whenever number of quarter-cycles are necessary.

Then it is easy enough to determine the number of quarter-cycles required (just count the complete cycles and note whether the pendulum is moving toward or away from its position of release at the instant the cart hits the obstacle; the rest is easy to reason out).
It is probably easiest to focus your eyes on the pendulum and your ears on the sound of the cart hitting the obstacle.

Timing of other events is done in a similar manner.