Expression for time period
Time period is related to the acceleration and displacement of the simple pendulum by the following equation.
![](https://mashalscienceacademy.com/wp-content/uploads/2023/06/Time-period-1.png)
Similarly,
![](https://mashalscienceacademy.com/wp-content/uploads/2023/06/Time-period-2.png)
The LHS of the two equations are equal and the RHS must also be.
![](https://mashalscienceacademy.com/wp-content/uploads/2023/06/Time-period-3.png)
Cancelling negative sign and displacement x on both sides and simplifying,
![](https://mashalscienceacademy.com/wp-content/uploads/2023/06/Time-period-4.png)
Taking reciprocals of both sides,
![](https://mashalscienceacademy.com/wp-content/uploads/2023/06/TIme-period-5.png)
Taking square-roots of both sides,
![](https://mashalscienceacademy.com/wp-content/uploads/2023/06/Time-period-6.png)
![](https://mashalscienceacademy.com/wp-content/uploads/2023/06/Time-period-7.png)
This is expression for the time period of the simple pendulum.