The pendulum

If a pendulum has length l, then the period T of swing (to and fro) is given by where g denotes the acceleration produced by gravity (980 cm/sec2).

For a pendulum clock, the speed at which the clock runs is governed by the length of the pendulum. 

• How would you adjust the pendulum to correct a clock that was running a little fast?

•  What would happen if the length of the pendulum were doubled? halved?                                        
• If a pendulum clock were taken to the moon (for which the value of g is less), how would the pendulum length need to be altered for the clock to run at the correct speed?

                                        

In the formula  we notice that the
period T is proportional to the length l.
This means that T decreases when l decreases,
and T increases when l increases.

• So to correct a clock that is running a little fast,
we wish to increase T. Hence we increase l a little.

•  If the length of the pendulum is doubled,
l is replaced by 2l.
This means that T is increased by a factor of 2.
Similarly, if l is halved, T is decreased;
the new value is T /2.


In the formula  we notice that the
period T is inversely proportional to the gravity g.
This means that for a given, fixed length l,
T increases when g decreases.

• So if T is to remain the same when the clock
is on the moon, the length l will also
have to be decreased,
and in fact proportionally to the change in gravity.