In given figure, a body of mass M is held between two massless springs, on a smooth inclined pl

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13.Oscillations

hard

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

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

B

$\frac{1}{2 \pi} \sqrt{\frac{2 k }{ Mg \sin \alpha}}$

C

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

D

$\frac{1}{2 \pi} \sqrt{\frac{ k }{ Mg \sin \alpha}}$

(JEE MAIN-2021)

Solution

$K _{ eq }= K _{1}+ K _{2}= K + K =2 K$

$T =2 \pi \sqrt{\frac{ m }{ K _{ eq }}}=2 \pi \sqrt{\frac{ m }{2 K }}$

$f =\frac{1}{ T }=\frac{1}{2 \pi} \sqrt{\frac{2 K }{ m }}$

Standard 11

Physics

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