A simple example of a pendulum is a mass on a string. The forces on the mass are gravity and the string tension. Applying Newton's second law for rotation about the pivot point
Στ = Iα → - mg L sin θ = Iα
Note negative sign because torque is opposite to angular displacement.
For small angles we use the approximation: sin θ ≈ θ
This gives the small angles equation of motion: - mg Lθ ≈ Iα.
This equation of motion has the SHM form: - ω2θ = α.
|So the angular frequency is ω||=||(||
For a simple pendulum the rotational inertia is by: I = mL2
|This gives ω||=||(||
|)||½||independent of the pendulum mass.|