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Question

Four massless springs whose force constants are 2k, 2k, k and 2k respectively are attached to mass M kept on a frictionless plane (as shown in figure). If the mass M is displaced in the horizontal direction, then the frequency of the system is

A
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B
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C
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D
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Solution

The correct option is B
Springs on the left of the block are in series, hence their equivalent spring constant is K1=(2K)(2K)2K+2K=K
Springs on the right of the block are in parallel, hence their equivalent spring constant is K2=K+2K=3K.
Now again both K1and K2are in parallel
Keq=K1+K2=K+3K=4K
Hence, Frequency is f=12πKeqM=12π4KM

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