Consider a mass (m) attached to an end of a spiral spring (which obeys Hooke’s law) whose other end is fixed to a support as shown in Figure. The body is placed on a smooth horizontal surface. Let the body be displaced through a distance x towards right and released. It will oscillate about its mean position. The restoring force acts in the opposite direction and is proportional to the displacement.

Restoring force F = – kx.

From Newton’s second law, we know that F = ma

So, ma = – kx

So, **a = (-k/m)*x**

Comparing with the equation of simple harmonic motion, **a = – ω ^{2}x**

We get, **ω ^{2} = (k/m)**

Or, ω = √( k/m)

But, T = 2π/ω

Time period = **T = 2π √( m/k)**

And frequency, **n = 1/T = 1/2π [√( k/m)]**