DOES IT MEAN THAT THE MOTION OF THE PENDULUM SIMPLE HARMONIC? For a simple pendulum, the pendulum swing back and forth in a period motion… So…

First, let’s look at simple harmonic motion… For a simple harmonic motion, the acceleration equation is expressed as a = - ω² x knowing that ω is a constant value, the acceleration of mass is directly proportional to the displacement x.

we can rewrite the tangential acceleration as a t = - gsin(s/L) In a simple pendulum, the tangential acceleration is expressed as - gsinθ = a t according to the formula s = Lθ, where s is the arc length, L is the length of the string.

Let’s compare the acceleration equation in simple harmonic motion and the acceleration equation in simple pendulum… a t = - gsin(s/L) and a = - ω² x Notice that the acceleration in simple pendulum is not proportional to displacement, instead, it is proportional to sin(s/L). Therefore, pendulum motion is NOT simple harmonic motion.