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 at = - gsin(s/L)

In a simple pendulum, the tangential acceleration is expressed as - gsinθ = at

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…

at = - gsin(s/L) and a = - ω² xNotice 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.