# Is a simple pendulum simple harmonic motion?

I'm wondering this because my textbook says that for small angles it is, but we learned that for simple harmonic motion to occur there must be a linear restoring force.. eg F= -kx.. but for the simple pendulum the restoring force is F= -mgsin(theta).. wouldn't this not be linear?

rock.freak667
Homework Helper
Well you see for small angles θ, sinθ≈θ so that the restoring force is F=-mgθ.

And now you know θ=x/l (x=arc length and l=length of pendulum)

so F=-mgx/l

Ohh okay, makes sense. Thank you!