Question

Derive time period of the simple pendulum.

Answer 1

You need to remember the formula constant of simple pendulum such that:

k = $\frac{L}{T^2}$

You need to consider the value of constant equivalent to $\frac{g}{{4\pi }^2}$ (g expresses the gravity acceleration)

You need to set the equations $\frac{g}{{4\pi }^2}$ and $\frac{L}{T^2}$ equal such that:

$\frac{L}{T^2}$ = $\frac{g}{{4\pi }^2}$

You need to find time period such that:

g $\times$ $T^2$ = 4 ${\pi }^2$ $\times$ L

$T^2$ = $\frac{{4\pi \times L}^2}{g}$
$\Rightarrow$ T = 2$\pi$ $\sqrt{\frac{L}{g}}$