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:  ω^{2}θ = α.
So the angular frequency is ω  =  ( 

)  ^{½} 
For a simple pendulum the rotational inertia is by: I = mL^{2}
This gives ω  =  ( 

)  ^{½}  independent of the pendulum mass. 