Question

For the mass on the spring, how is the period of the harmonic motion related to the spring constant, k?

Answer 1

Suppose a mass of `m` is attached to a spring of spring constant `K` is lying on a horizontal floor,then you pull the mass such that the spring got stretched by `x`,so restoring force acting on the mass due to the spring is `F=-Kx`

We can compare this with equation of S.H.M i.e `F=-momega^2x`

So,we get, `K=m omega^2`

So, `omega =sqrt(K/m)`

Hence time period is `T=(2pi)/omega =2pi sqrt(m/K)`