On earth, you swing a simple pendulum in simple harmonic motion with a period of 1.6 seconds. what is the period of this same pendulum on the moon? assume the moon's acceleration due to gravity is 1/6 of the acceleration due to gravity on earth.

The period of a simple pendulum is given by

where
L is the pendulum length
g is the acceleration of gravity

If we move the same pendulum from Earth to the Moon, its length L remains the same, while the acceleration of gravity g changes. So we can write the period of the pendulum on Earth as:

where  is the acceleration of gravity on Earth, while the period of the pendulum on the Moon is

where  is the acceleration of gravity on the Moon. 

If we do the ratio of the two periods, we get

but the gravity acceleration on the Moon is 1/6 of the gravity acceleration on Earth, so we can write  and we can rewrite the previous ratio as


so the period of the pendulum on the Moon is