Seconds Pendulum
A seconds pendulum (also called as Royal Pendulum) is a pendulum whose time period is 2 seconds; one second for swing in one direction and one second for returning swing. Eg: The pendulum of the clock. The time period of seconds pendulum depends upon the length of the string of the pendulum (T∝L). On Earth the length of the seconds pendulum is 0.994m ≈ 1m.
The length of seconds pendulum is calculated by the following formula.
\[L=\dfrac{g}{{\pi}^{2}}\]
(Where L=length and g=gravity)
We know that value of gravity on earth is 9.81 so let's calculate the length of seconds pendulum on Earth.
Calculation
\[L=\dfrac{9.81}{{\pi}^{2}}=\dfrac{9.81}{{3.142}^{2}}=\dfrac{9.81}{9.872}=0.994\]
⇒ Hence the length of seconds pendulum on Earth is 0.994m
Now let's calculate the length of seconds pendulum on Moon.
Note: Gravity on moon is 1/6 of gravity on Earth (1.62 m/s2)
Calculation
\[L=\dfrac{1.62}{{\pi}^{2}}=\dfrac{1.62}{{3.142}^{2}}=\dfrac{1.62}{9.872}=0.164\]
⇒ Hence the length of seconds pendulum on the moon is 0.164 m
Meanings
1. Time Period of pendulum: The time required to complete 1 oscillation (one cycle).