The Linear Spring-Mass System

Classical Mechanics Level 5

A Mass $\displaystyle m$ is attached to a spring of mass $\displaystyle M$ and spring constant $\displaystyle K$ .

If the velocity of the mass $\displaystyle m$ varies linearly over the length of the spring when it is given a kick, Let $\displaystyle T$ denote the Time Period of the system.

Find $\displaystyle 1000T$ to the nearest integer.

Details and Assumptions:
$\bullet m = 3Kg$
$\bullet M = 0.5Kg$
$\bullet K = 100N/m$