Rods with Springs!

Classical Mechanics Level 5

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4 identical bars of mass \(M\) and length \(L\) are connected by pins at \(A,B, C\) and \(D\). The bars are attached to four massless springs of same spring constant \(K\). The entire system can move in horizontal plane. In the equilibrium position \(\theta = 45^\circ\) as shown in figure. If the corners \(A\) and \(C\) are given a slight displacement away from each other and released, find angular frequency of small oscillations.

Details and Assumptions:

  • There is no friction anywhere.
  • \(M = 3 \text{ kg}\).
  • \(L = 1 \text{ m}\).
  • \(K = 200 \text{ N/m}\).

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