Question

On a smooth inclined plane, a body of mass $M$ is attached between two springs. The other ends of the springs are fixed to firm supports. If each spring has force constant $k$, the period of oscillation of the body(assuming the springs as massless) is

• A. $2\pi \sqrt{\frac{M}{2k}}$
• B. $2\pi \sqrt{\frac{2M}{k}}$
• C. $2\pi \sqrt{\frac{M\sin \theta }{2k}}$
• D. $2\pi \sqrt{\frac{2Mg}{k}}$

Answer 1

The correct option is B $2\pi \sqrt{\frac{2M}{k}}$

The two spring are in series, so the effective spring constant is $K^{-1}=\frac{1}{k}+\frac{1}{k}=\frac{2}{k}$.

Frequency of oscillation is $\omega =\sqrt{K/M}=\sqrt{\frac{k}{2M}}$

Thus, the period of oscillation is $T=2\pi /\omega =2\pi \sqrt{\frac{2M}{k}}$