Physics
Explainer
Why Springs Oscillate: Simple Harmonic Motion
A pendulum's period barely depends on how far you swing it. Why?
Quick check · tap an answer to continue
Lesson notes
Key points
- Simple harmonic motion happens whenever the restoring force is proportional to displacement and points back toward equilibrium.
- Combining F equals minus kx with Newton's second law gives a differential equation whose solutions are sines and cosines.
- The angular frequency omega equals the square root of k over m, so amplitude never enters the period.
- A pendulum only approximates this for small angles, where sine theta is close to theta, making gravity's pull linear.
Takeaway: Linear restoring force means period is set by k and m, not amplitude.
Quick check: Doubling a mass on a spring changes the period by a factor of?
- 2
- √2
- 1/2
Restoring forceEquation of motionAngular frequencySmall-angle approximation
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