Why is the pendulum a good example of simple harmonic motion? Under what conditions the pendulum could not be used as a good example of simple harmonic motion?

The motion of a simple pendulum is very close to Simple Harmonic Motion (SHM). SHM results whenever a restoring force is proportional to the displacement, a relationship often known as Hooke's Law when applied to springs. Where F is the restoring force, k is the spring constant, and x is the displacement.

where θ is the angle the pendulum makes with the vertical. For small angles, sin(θ)∼θ, which would then lead to simple harmonic motion. For large angles, this approximation no longer holds, and the motion is not considered to be simple harmonic motion.

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