Simple Harmonic Motion wedge

A smooth wedge of mass mm and angle of inclination θ=60 °\theta = \SI{60}{\degree} is attached to two springs of spring constant kLk_\textrm{L} on the left, and kR=3kLk_\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=3 kgm=\SI{3}{\kilo\gram}
  • kL=18N/mk_\textrm{L}= \frac18 \si[per-mode=symbol]{\newton\per\meter}.
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