Question 126 of 194

In the given figure, a body of mass $M$ is held between two massless springs, on a smooth inclined plane. The free ends of the springs are attached to firm supports. If each spring has spring constant $k,$ the frequency of oscillation of given body is:

A$\dfrac{1}{2\pi }\sqrt{\dfrac{2k}{Mg\sin \alpha }}$B$\dfrac{1}{2\pi }\sqrt{\dfrac{k}{Mg}\sin \alpha }$C$\dfrac{1}{2\pi }\sqrt{\dfrac{k}{2M}}$D$\dfrac{1}{2\pi }\sqrt{\dfrac{2k}{M}}$

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Answer: (D) $\dfrac{1}{2\pi }\sqrt{\dfrac{2k}{M}}$

${K}_{eq}={K}_{1}+{K}_{2}=K+K=2K$
$T=2\pi \sqrt{\dfrac{m}{{K}_{eq}}}=2\pi \sqrt{\dfrac{m}{2K}}$
$f=\dfrac{1}{T}=\dfrac{1}{2\pi }\sqrt{\dfrac{2K}{m}}$