Question:

Why is the period of oscillation independent of amplitude of oscillation?

Answer:

All simple harmonic motions can be shown mathematically to have a natural frequency. This natural frequency depends on the stiffness and inertia of the oscillataory system. What surprises some people is the natural frequency is not affected by the amplitude of oscillation.

Some people jump to the conclusion that a pendulum with a longer length should have a longer period since the distance it travels per oscillation is longer, overlooking the fact that a longer pendulum also gets to accelerate to a higher maximum speed. And it so happens that these two factors ( higher speed and longer distance) cancel each other out exactly.

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