Is a simple pendulum simple harmonic motion?

AI Thread Summary
A simple pendulum exhibits simple harmonic motion (SHM) when the angle is small, as the restoring force can be approximated as linear. While the general restoring force for a pendulum is F = -mg sin(θ), for small angles, sin(θ) can be approximated by θ, leading to F = -mgθ. This approximation allows the force to be expressed as F = -mgx/l, aligning it with the form required for SHM. Thus, the conditions for SHM are satisfied under these circumstances. Understanding this relationship clarifies the connection between pendulum motion and simple harmonic motion.
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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?
 
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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!
 

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