# Second's Pendulum

A second's pendulum is a pendulum whose time period is exactly two seconds, one second for the swing to one side and one second for the return swing. It is used in pendulum clocks to measure time intervals. The length of a second's pendulum is approximately one metre.

## Frequency of a second's pendulum

The frequency of a second's pendulum is given by
\begin{align}
\nu=\frac{1}{T}=\frac{1}{2}\;\mathrm{Hz}.
\end{align}

## Length of a second's pendulum

The second's pendulum is a simple pendulum with time period $T=2$ seconds. The time period of a simple pendulum is related to its length $l$ by
\begin{align}
T=2\pi\sqrt{\frac{l}{g}}.
\end{align}
Thus, the length of second's pendulum on the equator ($g=9.81$ m/s^{2}) is
\begin{align}
l &=\frac{T^2 g}{4\pi^2}=\frac{(2)^2(9.81)}{4(3.14)^2} \\
&=0.995\,\mathrm{m}=995\,\mathrm{mm}.
\end{align}

## Problems from IIT JEE

**Problem (JEE Mains 2021) **
**Statement 1:** A second's pendulum has a time period of 1 s.

**Statement 2:** It takes precisely one second to move between the two extreme positions.

- Both statement 1 and statement 2 are true.
- Both statement 1 and statement 2 are false.
- Statement 1 is true but statement 2 is false.
- Statement 1 is false but statement 2 is true.

## Related

- Simple Harmonic Motion
- Physical Pendulum
- Torsional Pendulum

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