Check out some examples we would see in the lab for Simple harmonic motion (SHM). A normal spring is the prime example of this motion, where the restoring force depends on the displacement from equilibrium. A spring is F = -kx. So check these out, and we'll figure out the math in class or in the following videos:
SHM for a pendulum (small angle approximation)
SHM for a swinging stick (small angle approx.)
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