Simple Spring - Hooke's Law

A simple spring with a mass m displaced by a distance d from its equilibrium point, and released, will oscillate with simple harmonic motion.

Hooke's Law for springs says that the force is equal to the displacement times the spring constant. The minus sign tells us this is a restorative force.

F = -k d (1)

k is the spring constant in Newtons per meter, and d is the displacement from equilibrium in meters.

Newton's second law tells us force equals mass times acceleration, or

F=ma (2)

Combining (1) and (2) we get ma = -kd, and so

a = -kd/m

The frequency f (in Hertz) of the oscillations is given by

1/2PI * sqrt(k/m)

Note that the frequency is independent of the displacement. Also, real springs have a practical displacement range, beyond which the spring constant no longer holds, and the spring looses its restorative properties.


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