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Simple harmonic motion
Beginner
Restoring force proportional to displacement.
F = −kxSHM occurs when the restoring force is proportional and opposite to displacement, F = −kx. The motion is sinusoidal, and its period doesn't depend on amplitude.
A mass on a spring, small-angle pendulum.
F ∝ −x is the key test.
In more detail
Simple harmonic motion occurs when the restoring force is proportional to displacement and opposite to it. The result is sinusoidal motion with a constant period, independent of amplitude.
Real-world uses
- A mass on an ideal spring is the standard example of SHM.
- Small oscillations of many systems are approximately SHM.
- Engineers design car suspensions and seismometers around simple harmonic motion, where the restoring force is proportional to displacement.
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Frequently asked questions
Why is SHM so important?
Many systems behave like SHM for small displacements, which makes it a powerful approximation.
What is the equation of motion?
x'' = −ω²x, where ω is the angular frequency.
Why does the force have a minus sign?
It points back toward equilibrium, opposite to the displacement, which is what makes the motion oscillate.
Related topics in Oscillations & SHM
Periodic motion · Oscillatory motion · Period, frequency, amplitude · SHM displacement · SHM velocity · SHM acceleration