As shown in the figures, a uniform rod O O^ of length l is hinged at the point O and held in place vertically between two walls using two massless springs of same spring constant. The springs are connected at the midpoint and at the top-end (O^ ) of the rod, as shown in Fig. 1 and the rod is made to

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As shown in the figures, a uniform rod O O^ of length l is hinged at the point O and held in place vertically between two walls using two massless springs of same spring constant. The springs are connected at the midpoint and at the top-end (O^ ) of the rod, as shown in Fig. 1 and the rod is made to oscillate by a small angular displacement. The frequency of oscillation of the rod is f_1. On the other hand, if both the springs are connected at the midpoint of the rod, as shown in Fig. 2 and the rod is made to oscillate by a small angular displacement, then the frequency of oscillation is f_2. Ignoring gravity and assuming motion only in the plane of the diagram, the value of f_1 f_2 is:

Quantrex Academy · Accepted Answer

Correct answer: C. 5 2

aligned & ML ^2 3 + K 2 2 + K =0 \ & + 15 4 k M =0 \ & =- ( 15 4 k M ) \ & _1= 15 ~K 4 M aligned 1 3 ML ^2 +2 ~K ~L 2 ~L 2 =0 aligned & + 3 2 K M =0 \ & =- 3 2 K M \ & _2= 3 2 K M \ & _1 _2 = 15 4 2 3 = 5 2 aligned

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