Question

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

• A. $\frac{1}{2\pi }\sqrt{\frac{2K}{Mg\sin \alpha }}$
• B. $\frac{1}{2\pi }\sqrt{\frac{K}{Mg\sin \alpha }}$
• C. $\frac{1}{2\pi }\sqrt{\frac{2K}{M}}$
• D. $\frac{1}{2\pi }\sqrt{\frac{K}{2M}}$

Answer 1

The correct option is C $\frac{1}{2\pi }\sqrt{\frac{2K}{M}}$

$K_{eq}=K+K=2K$

Now, $T=2\pi \sqrt{\frac{M}{K_{eq}}}$

$\Rightarrow T=2\pi \sqrt{\frac{M}{2K}}$

$\Rightarrow f=\frac{1}{2\pi }\sqrt{\frac{2K}{M}}$