• # question_answer A mass M is suspended from a light spring. An additional mass m added displaces the spring further by a distance x. Now the combined mass will oscillate on the spring with period A) $T=2\pi \sqrt{\frac{mg}{x(M+m)}}$      B) $T=2\pi \sqrt{\frac{(M+m)x}{mg}}$ C) $T=\frac{\pi }{2}\sqrt{\frac{mg}{x(M+m)}}$      D) $T=2\pi \sqrt{\frac{M+m}{mg}}$

Let elongation in spring is ${{x}_{0}}$ when M is suspended, then $Mg=k{{x}_{0}}$ $(M+m)g=K({{x}_{0}}+x)\Rightarrow kx=mg$ Time period of combined mass,$T=2\pi \sqrt{\frac{M+m}{K}}$$\Rightarrow$$T=2\pi \sqrt{\frac{(M+m)x}{mg}}$