This approximation is accurate only for small angles because of the expression for angular acceleration α being proportional to the sine of the displacement angle: − − m g l sin ⁡ ⁡ θ θ = I α α , where I is the moment of inertia. When θ is small, sin θ ≈ θ and therefore the expression becomes − − m g l θ θ = I α α which makes angular acceleration directly proportional and opposite to θ, satisfying the definition of simple harmonic motion (that net force is directly proportional to the displacement from the mean position and is directed towards the mean position).