Four massless springs whose force constants a | vedclass

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(B) The two springs on the left side,each having a spring constant of $2k$,are connected in series. Their equivalent spring constant $k_{eq1}$ is give

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

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(B) The two springs on the left side,each having a spring constant of $2k$,are connected in series. Their equivalent spring constant $k_{eq1}$ is given by:$\frac{1}{k_{eq1}} = \frac{1}{2k} + \frac{1}{2k} = \frac{2}{2k} = \frac{1}{k} \implies k_{eq1} = k$.The two springs on the right side of mass $M$ are connected in parallel. Their effective spring constant $k_{eq2}$ is:$k_{eq2} = k + 2k = 3k$.Now,the mass $M$ is connected to these two equivalent systems ($k_{eq1}$ and $k_{eq2}$) in parallel. Therefore,the net equivalent spring constant $k_{net}$ of the system is:$k_{net} = k_{eq1} + k_{eq2} = k + 3k = 4k$.The frequency of oscillation $f$ for a spring-mass system is given by:$f = \frac{1}{2\pi}\sqrt{\frac{k_{net}}{M}} = \frac{1}{2\pi}\sqrt{\frac{4k}{M}}$.

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 figure). If the mass $M$ is displaced in the horizontal direction,then the frequency of oscillation of the system is

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