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(B) $1$. The two springs on the left with force constants $2k$ and $2k$ are in series. Their equivalent spring constant $k_{L}$ is given by $\frac{1}{

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

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(B) $1$. The two springs on the left with force constants $2k$ and $2k$ are in series. 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 $k_{L} = k$.$2$. The two springs on the right with force constants $k$ and $2k$ are in parallel. Their equivalent spring constant $k_{R}$ is given by $k_{R} = k + 2k = 3k$.$3$. The left and right combinations are effectively in parallel with respect to the mass $M$. Thus,the total effective spring constant $k_{eff} = k_{L} + k_{R} = k + 3k = 4k$.$4$. The frequency of oscillation $f$ 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 the mass $M$ is displaced in the horizontal direction,then the frequency of oscillation of the system is:

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