Question

What is the frequency of a pendulum?

Answer 1

Hint: In order to calculate the frequency of a pendulum, we should know about simple pendulum and term frequency. A simple pendulum consists of a long string with its one end fixed at some point vertically and a bob of some mass is held at its other end and it is free to move about its mean position if displaced through some distance, then the motion governed by simple pendulum is oscillatory motion, and frequency is the measurement of number of oscillation made by a body in one second.

Complete step by step answer:
An oscillatory motion is one in which the body oscillates between two fixed points and a simple pendulum oscillates between its two extreme points when it is released.The time period of a simple pendulum of string having length of $L$ is calculated as,
\[T = 2\pi \sqrt {\dfrac{L}{g}} \]
Where $g$ is the acceleration due to gravity which has a definite value on earth as $g = 9.8\,m{s^{ - 2}}$.

And, we know that inverse of time period is known as frequency because frequency is the measure of number of oscillation per second so, frequency of simple pendulum is given by
\[\therefore f = \dfrac{1}{{2\pi }}\sqrt {\dfrac{g}{L}} \]

Hence, the frequency of a simple pendulum is \[f = \dfrac{1}{{2\pi }}\sqrt {\dfrac{g}{L}} \].

Note: It should be remembered that a pendulum which just consists of a string and a bob attached to it is known as a simple pendulum and the SI unit of frequency is known as Hertz denoted by Hz. Every periodic motion or oscillatory motion has frequency and we can say that frequency of pendulum is independent of mass of the bob and it only depends upon acceleration due to gravity and length of the string.