Mathematics I / Oscillations and Periodic Motion
Practice question · True or false

Doubling the amplitude of an ideal spring oscillator leaves its period unchanged.

Hints
  1. What does the period depend on?
  2. T=2πm/kT = 2\pi\sqrt{m/k}, no amplitude in it.
Show the answer

True

Why

True. T=2πm/kT = 2\pi\sqrt{m/k} contains no amplitude term: a wider swing covers more distance at proportionally higher speed and takes the same time. This isochronism is what makes pendulum clocks possible, and it holds only while the restoring force stays proportional to displacement, real springs lose it when stretched far.

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