The system in figure lies on a frictionless horizontal table. Both masses are m, and the two spring constant are nK (where n is a numerical factor) and K as shown in figure. the springs have the same relaxed length. Assuming that it is possible to set up initial conditions so that the masses oscillate back and forth with the two springs always having equal lengths at any given instant. Choose CORRECT statement(s)

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Relative to mean position, if displacement of left mass is x, then displacement of right mass is x.

Value of n is $\frac{2}{3}$

Relative to mean position, if displacement of left mass is x, then displacement of right mass is 2x.

Value of n is $\frac{3}{2}$

answer is A, C.

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Detailed Solution

$(n - 1) K x = m ω^{2} x, K x = m ω^{2} 2 x n - 1 = \frac{1}{2} n = \frac{3}{2}$

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