Question 705049

SCQHARD

Three identical simple pendula (of mass mm and equilibrium string length ll) are attached together by springs of spring constant kk as shown in the figure. The frequencies of small oscillations are given by g/l,g/l+k/m,g/l+3k/m\sqrt{g/l}, \sqrt{g/l + k/m}, \sqrt{g/l + 3k/m}.

The normal modes (without normalisation) corresponding to these frequencies, respectively, are

Question
(A)

(1,1,1),(1,0,1),(1,−2,1)(1, 1, 1), (1, 0, 1), (1, -2, 1)

(B)

(1,1,1),(1,0,−1),(1,−2,1)(1, 1, 1), (1, 0, -1), (1, -2, 1)

(C)

(1,1,1),(1,0,−1),(1,2,1)(1, 1, 1), (1, 0, -1), (1, 2, 1)

(D)

(1,2,1),(1,0,−1),(1,1,1)(1, 2, 1), (1, 0, -1), (1, 1, 1)

Detailed Solution

If we ignore the pendulum part then the system will reduce to a linear triatomic molecular chain with normal modes (1,1,1),(1,0,−1),(1,−2,1)(1, 1, 1), (1, 0, -1), (1, -2, 1) corresponding to the frequencies provided.

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