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(B) On the right side of the block,two springs with force constants $K$ and $2K$ are connected in parallel to the wall. Their equivalent spring consta

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$\frac{1}{2 \pi} \sqrt{\frac{4 K}{M}}$

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(B) On the right side of the block,two springs with force constants $K$ and $2K$ are connected in parallel to the wall. Their equivalent spring constant is $K_R = K + 2K = 3K$.On the left side of the block,two springs with force constants $2K$ and $2K$ are connected in series to the wall. Their equivalent spring constant $K_L$ is given by $\frac{1}{K_L} = \frac{1}{2K} + \frac{1}{2K} = \frac{2}{2K} = \frac{1}{K}$,so $K_L = K$.Since the block is between these two sets,the effective spring constant of the system is $K_{eff} = K_R + K_L = 3K + K = 4K$.The frequency of oscillation is given by $f = \frac{1}{2 \pi} \sqrt{\frac{K_{eff}}{M}} = \frac{1}{2 \pi} \sqrt{\frac{4K}{M}}$.

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

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