# A mass m is suspended from a spring of force constant k and just touches another identical spring fixed to the floor…

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

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