Question

A pendulum makes 40 oscillations in 4 seconds. Find its time period.

Answer 1

A simple pendulum is a point mass suspended from a fixed support and attached to a light inextensible string. The mean position of a simple pendulum is the vertical line passing through the fixed support. The length of the simple pendulum, denoted by L, is the vertical distance between the point of suspension and the suspended body's centre of mass (when it is in the mean position).

Complete step by step solution:
A pendulum's time period is denoted by the letter "T" and is defined as the time the pendulum takes to complete one full oscillation.
The process of repeating variations of any quantity or measure about its equilibrium value in time is known as oscillation. A periodic variation of a matter between two values or around its central value is also known as oscillation.
A pendulum completes one oscillation when it begins at one extreme position A, moves to the other extreme position B, and then returns to A. The time period is the amount of time it takes to complete one oscillation. The oscillation's time period remains constant.
Given: -
No. of oscillations $= 40$
time taken $= 4\sec$
To find: - Time period of the pendulum
time period =$\dfrac{{time taken}}{{no.of oscillations}}$
time period $= \dfrac{4}{{40}}$
$= \dfrac{1}{{10}}$of a second.
Hence, the time period of the pendulum is $\dfrac{1}{{10}}$of a second.

Note:
The frequency of a pendulum is the number of times it swings back and forth in a given period of time. For instance, in 60 seconds, how many times does the pendulum swing back and forth? The length of the pendulum determines its frequency. It means that if the pendulum is shorter, the swing rate will be higher.