Is a simple pendulum simple harmonic motion?

[maccha]

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]

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

 

[maccha]

Ohh okay, makes sense. Thank you!