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1. The shown arrangement is in a horizontal plane. The particle with mass m is restricted to move in an elliptical orbit with shown dimension. The particle has velocity v at the shown position towards right. Length of rod is 2l. The coefficient of restitution between the particle and the rod is 1/3. The moment of inertia of rod is I, about O. i. Find the locus of mid-point of spring of force constant K 3 . ii. Find the frequency of the rod. iii. What would be the maximum angular displacement of the oscillating system. (Assume only one collision)


1.     The shown arrangement is in a horizontal plane. The particle with mass m is restricted to move in an elliptical orbit with shown dimension. The particle has velocity v at the shown position towards right. Length of rod is 2l. The coefficient of restitution between the particle and the rod is 1/3. The moment of inertia of rod is I, about O.


                      i.        Find the locus of mid-point of spring of force constant K3.


                     ii.        Find the frequency of the rod.


                    iii.        What would be the maximum angular displacement of the oscillating system.


(Assume only one collision)


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