Question: Derive expressions for the time period and frequency of a simple pendulum.
Expression for time period
Time period is related to the acceleration and displacement of the simple pendulum by the following equation.
Similarly,
The LHS of the two equations are equal and the RHS must also be.
Cancelling negative sign and displacement x on both sides and simplifying,
Taking reciprocals of both sides,
Taking square-roots of both sides,
This is expression for the time period of the simple pendulum.
Expression for the frequency of the simple pendulum
Since, therefore, put value of T from the above equation,
This is expression for the frequency of simple pendulum.