Q.
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 support. If each spring has force constant k, the period of oscillation of the body (assuming the springs as massless) is
A) $2\pi\lbrack M/2k\rbrack$$^{1/2}$
B) $2\pi\lbrack 2M/k\rbrack$$^{1/2}$
C) $2\pi\lbrack Mg\sin\theta/2k\rbrack$$^{1/2}$
D) $2\pi\lbrack 2Mg/k\rbrack$$^{1/2}$
Explanation
(a) It is a system of two springs in parallel. The restoring force on the body is due to springs and not due to gravity pull. Therefore slope is irrelevant. Here the effective spring constant$= k + k = 2k$
Thus time period, $T = 2\pi\sqrt{M/2k}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.