In a grandfather clock, the second hand moves forward by one second for each half period of the clock’s pendulum.
a. how long would you expect the pendulum to be in a grandfather clock?
b. if you took a grandfather clock to the moon, where gravity is 1/6 earth’s gravity, what would you expect to happen to the period of the clock?
c. what happens to the apparent passage of time on the moon?

To solve the problem it is necessary to take into account the concepts related to simple pendulum, i.e., a point mass that is suspended from a weightless string. Such a pendulum moves in a harmonic motion -the oscillations repeat regularly, and kineticenergy is transformed into potntial energy and vice versa.

In the given problem half of the period is equivalent to 1 second so the pendulum period is,

From the equations describing the period of a simple pendulum you have to

Where

g= gravity

L = Length

T = Period

Re-arrange to find L we have

Replacing the values,

In the case of the reduction of gravity because the pendulum is in another celestial body, as the moon for example would happen that,

In this way preserving the same length of the rope but decreasing the gravity the Period would increase considerably.

at positions a, g kinetic energy is maximum.

at position d, potential energy is maximum.