In the figure is shown, a plate of mass $60g$ at rest and in equilibrium. A particle of mass $30g$ is released from a height $\frac{4.5mg}{k}$ from the plate. The particle sticks to the plate. Spring has force constant $100N{m}^{-1}$. Neglecting the duration of collision, the time from the collision of the particle and the plate to the moment when the spring has maximum compression is $\left(10\beta \pi \right)$ millisecond. Find the value of $\beta$.(m= mass  of particle)