On Earth, the period of a pendulum is given by:
[tex]T_{earth}=2\pi \sqrt{ \frac{L}{g_{earth} } [/tex]
where L is the length of the pendulum and [tex]g_{earth}=9.81~m/s^2[/tex] is the gravitational acceleration on Earth.
Similarly, the period of the same pendulum on Mars will be
[tex]T_{mars}=2\pi \sqrt{ \frac{L}{g_{mars} } [/tex]
where [tex]g_{mars}=3.71~m/s^2[/tex] is the gravitational acceleration on Mars.
Therefore, if we want to see how does the period of the pendulum on Mars change compared to the one on Earth, we can do the ratio between the two of them:
[tex] \frac{T_{mars}}{T_{earth}}= \sqrt{ \frac{g_{earth}}{g_{mars}} } = \sqrt{ \frac{9.81~m/s^s}{3.71~m/s^2} }=1.63 [/tex]
Therefore, the period of the pendulum on Mars will be 1.63 times the period on Earth.
