Q: A mass *m* is suspended from a spring of force constant k and just touches another identical spring fixed to the floor as shown in the figure. The time period of small oscillations is

(a) $ \displaystyle 2\pi \sqrt{\frac{m}{k}} $

(b) $ \displaystyle \pi \sqrt{\frac{m}{k}} + \pi \sqrt{\frac{m}{k/2}}$

(c) $\displaystyle \pi \sqrt{\frac{m}{3k/2}} $

(d) $ \displaystyle \pi \sqrt{\frac{m}{k}} + \pi \sqrt{\frac{m}{2k}}$

Ans: (d)

Sol: T = t_{1}+ t_{2 , }Where t_{1}= time period of system of two spring in parallel & t_{2} = time period of Single spring block system

$ \displaystyle T = \pi \sqrt{\frac{m}{k}} + \pi \sqrt{\frac{m}{2k}}$