Question

Show that acceleration is directly proportional to the displacement in simple pendulum

Answer 1

Let the equation of SHM, 

$$x=A\sin(ωt)\\v=Aω\cos(ωt)\\a=−Aω ^ 2 \sin(ωt) ⇒a=−ω^ 2 x$$

Acceleration is directly proportional to displacement of the particle from the mean position.