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

=

(

m g L I

)

½

For a simple pendulum the rotational inertia is by:   I = mL²

This gives   ω

=

(

g L

)

½

independent of the pendulum mass.