Question

a simple pendulum has a period of 7 seconds on earth. What would the approximate period be on the moon, where the gravity is approximately 1/6 as strong as on earth

Answer 1

recall if you assume a small angle displacement the period of a pendulum is T depends on only the Length of pendulum L and the gravity force g
\[T=2\pi*\sqrt{\frac{ L }{ g }}\]

Answer 2

period T=7 s, and earth gravity g=9.8 m/s^2
\[7 = 2\pi \sqrt{\frac{ L }{ 9.8 }}\]
\[L \approx 12.16~m\]
The pendulum has a length around 12.16 meters

Answer 3

1/6 earth gravity for the moon is g=9.8/6 m/s^2
now have the length L=12.16 ,

\[T=2\pi \sqrt{\frac{ 12.16 }{ (9.8/6) }}\approx 17.15~~s\]

Answer 4

Thank you very much!