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  4. 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 the system is

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Q. 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 the system isPhysics Question Image

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Solution:

Two springs on the L.H.S. of mass M are in series and two springs on the R.H.S. of mass M are in parallel. These combinations of springs will be considered in parallel to mass M. Thus effective spring constant,
$\quad\quad K=\frac{2k\times2k}{2\kappa+2k}+\left(k+2k\right)=4k$
$\therefore \quad Frequency υ = \frac{1}{2\pi}\sqrt{\frac{K}{M}}=\frac{1}{2\pi}\sqrt{\frac{4k}{M}}$

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