The periodic time of one oscillation for a simple pendulum is:

Explanation:

Here, we have for the ball to be in equilibrium

Tension in cord = mg cos θ

For small angle θ,

cos θ  = 1

So, F = mg sin θ

for the object in SHM

gθ = ω²x 

x = lθ

g = ω²lθ

\(g\theta = {\left( {\frac{{2\pi }}{T}} \right)^2}l\theta\)

\(T = 2π{ \sqrt{l \over g}}\)

Time Period of Simple Pendulum

• The time for completing one cycle is called a time period of a pendulum.
• The time period of the pendulum watch depends upon the length of the pendulum and independent of the mass of the bob.
•  \(T = 2π{ \sqrt{l \over g}}\) , where T = time period  L is the length of the pendulum and g is an acceleration of gravity.