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

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 $F = - K x$
We can compare this with equation of S.H.M i.e $F = - m {\omega}^{2} x$
So,we get, $K = m {\omega}^{2}$
So, $\omega = \sqrt{\frac{K}{m}}$
Hence time period is $T = \frac{2 \pi}{\omega} = 2 \pi \sqrt{\frac{m}{K}}$