# The Linear Spring-Mass System

**Classical Mechanics**Level 4

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:**

\(\bullet m = 3Kg\)

\(\bullet M = 0.5Kg\)

\(\bullet K = 100N/m\)