Question

On a smooth inclined surface 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 is

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Time period $T=2\pi \sqrt{\frac{x}{a}}$
If we displace the block by a distance ‘x’ upward then the restoring force will be
$F_{restoring}=2kx\Rightarrow a=\frac{2kx}{M}$
$T=2\pi \sqrt{\frac{x}{a}}=2\pi \sqrt{\frac{xM}{2kx}}=2\pi \sqrt{\frac{M}{2k}}$