Question

Define a simple pendulum. What is the time period of a pendulum? How does it vary with the length of a pendulum?

Answer 1

Simple pendulum

1. It is an arrangement consisting of a heavy solid spherical metallic bob suspended from fixed rigid support with the help of a weightless string and is free to oscillate about its mean position.
2. The distance from the centre of a spherical bob to the fixed point of suspension is called the effective length of the pendulum (l).

Time period:

1. The time taken by the pendulum to complete one oscillation ($\mathrm{O}\to \mathrm{A}\to \mathrm{B}\to \mathrm{C}\to \mathrm{D}$) is called time period of the pendulum.
2. It is denoted by T.
3. It is given by the formula,

$T=2\mathrm{\pi }\sqrt{\frac{\mathrm{l}}{\mathrm{g}}}$

Here l is the effective length of the pendulum and g is acceleration due to gravity.

Therefore, the time period of the pendulum varies directly with the square root of the length.