Question

A simple pendulum is constructed by hanging a heavy ball by a 5.0 m long string. It undergoes small oscillations. (a) How many oscillations does it make per second ? (b) What will be the frequency if the system is taken on the moon where acceleration due to gravitation of the moon is $1.67m{s}^{-2}$?

Answer 1

$L=5m$

$\left(a\right)T=2\pi \sqrt{\frac{l}{g}}$

$=2\pi \sqrt{\frac{5}{10}}$

$=2\pi \sqrt{0.5}=2\pi \left(0.7\right)$

$\therefore$ In $2\pi \left(0.7\right)sec,$ the body will complete

$\frac{1}{2\pi }\left(0.7\right)$ oscillation.

$\therefore f=\frac{1}{2\pi }\left(0.7\right)$

$=\frac{10}{14\pi }=\frac{0.70}{\pi }$ times

(b) When it is taken to the moon,

$T=2\pi \sqrt{\left(\frac{l}{g}\right)}$

Where $g\to$ Acceleration in the moon

$=2\pi \sqrt{\frac{5}{1.67}}$

$\therefore f=\frac{l}{T}$

$=\frac{1}{2\pi }\sqrt{\frac{1.67}{5}}=\frac{1}{2\pi }\left(0.557\right)$

$=\frac{1}{2\pi \sqrt{3}}$ times