# Question #5440f

Mar 18, 2016

A seconds pendulum is defined as a pendulum whose time period is exactly equal to 2 seconds.

#### Explanation:

Alternatively seconds pendulum has frequency equal to $\frac{1}{2} H z$. It takes one second to move from one extreme to the other while swinging and takes again one second for the return swing to the other end.

If we ignore air resistance, and for small swings we know that, time for one complete oscillation of a pendulum $T = 2 \pi \sqrt{\frac{L}{g}}$
where $L \mathmr{and} g$ are length of the pendulum and acceleration due to gravity respectively.
Therefore, length of Seconds pendulum ${L}_{\circ} = \frac{g}{\pi} ^ 2$,
inserting standard $g = 9.80665 m {s}^{-} 2$, We obtain its length as
$L = \frac{9.80665}{\pi} ^ 2 = 0.994 m$ rounded to third place of decimal.