Question

On a smooth inclined surface a body of mass $M$ is attached between two spring. The other ends of the springs are fixed to firm supports. If each spring ahs force constant $k$, the period of oscillation of the body is

• A. $2\pi {\left(\frac{2Mg}{k}\right)}^{1/2}$
• B. $2\pi {\left(\frac{M}{2K}\right)}^{1/2}$
• C. $2\pi {\left(\frac{2M}{k}\right)}^{1/2}$
• D. $2\pi \left(\frac{Mg\sin \theta }{2k}\right)$

Answer 1

The correct option is B $2\pi {\left(\frac{M}{2K}\right)}^{1/2}$

As we know,

$T=2\pi \sqrt{\frac{M}{K_{eff}}}$

now as spring block system is inclinesd ,only initial equillibrium position is changed , after achieving equillibrium, if a small displacement is given then it will behave as a simple spring block system.

now

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

so,

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