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 = t1+ t2 , Where t1= time period of system of two spring in parallel & t2 = time period of Single spring block system
$ \displaystyle T = \pi \sqrt{\frac{m}{k}} + \pi \sqrt{\frac{m}{2k}}$