When we consider the time period for small amplitude the motion

When we consider the time period for small amplitude the motion of the simple pendulum can be
approximated using simple harmonic motion i.e
F=mgsinθ (1)
Where F is the restoring force acting on the pendulum, M is it’s mass, g is the acceleration due to gravity
and θ is angular displacement. In addition for small θ,
Sin θ ≈ θ ( 2)
Hence, equation (1) reduces to
F≈ mgθ
(3)
Using Newton’s second law of motion we have that
F=mx”
(4)
In this case x= lsinθ = lθ if we consider (4) we also have x”=lθ” and also using (3)
and (4) we obtain
θ” =-g/l*θ
(5)
We then realize that this equation is the same as the equation of motion for the
simple harmonic motion