Simple Harmonic Motion wedge

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.
  • \(m=\SI{3}{\kilo\gram}\)
  • \(k_\textrm{L}= \frac18 \si[per-mode=symbol]{\newton\per\meter}\).
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