Question

Simple pendulum is system in which a bob is attached to a string and oscillates when it is disturbed from equilibrium. Suppose time period of oscillation of simple pendulum depends on length (l) of string, mass (m) of the bob, and acceleration due to gravity (g). Derive expression for its time period using method of dimensions.

Answer 1

The expression for the time period using method of dimensions is $T = [L]^{1/2}\times [LT^{-2}]^{-1/2}$.

Period of oscillation

The period of oscillation of a simple pendulum is the time taken for the pendulum to make a complete rotation.

The period of oscillation of a simple pendulum is calculated as;

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

where;

L is length (m)

g is acceleration due to gravity (m/s²)

The expression for the time period using method of dimensions is given as;

$T = [L]^{1/2}\times [LT^{-2}]^{-1/2}$

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