# Simple Harmonic Motion wedge

**Classical Mechanics**Level 5

A smooth wedge of mass \(m\) and angle of inclination \(\theta = \SI{60}{\degree}\) is attached to two springs of spring constant \(k_\textrm{L}\) on the left, and \(k_\textrm{R} = 3k_\textrm{L}\) on the right. The wedge rests on a smooth frictionless plane. Find the period of oscillation of the wedge in seconds.

Give your answer to 3 decimal places.

**Details and Assumptions**:

- The springs are perpendicular to the respective sides they are facing.
- The spring on the left is constrained to compress and extend along its length. It is attached to the wedge by a frictionless roller that can move along the hypotenuse.
- \(m=\SI{3}{\kilo\gram}\)
- \(k_\textrm{L}= \frac18 \si[per-mode=symbol]{\newton\per\meter}\).