Question

A mass $m$ is suspended from a spring of force constant $k$ and just touches another identical spring fixed to the floras shown in the figure. The time period of small oscillation is:

• A. $2\pi \sqrt{\frac{m}{k}}$
• B. $\pi \sqrt{\frac{m}{k}}+\pi \sqrt{\frac{m}{k/2}}$
• C. $\pi \sqrt{\frac{m}{3k/2}}$
• D. $\pi \sqrt{\frac{m}{k}}+\pi \sqrt{\frac{m}{2k}}$

Answer 1

The correct option is B $\pi \sqrt{\frac{m}{k}}+\pi \sqrt{\frac{m}{k/2}}$

The situation oscillate down to up as a two spring connected and from up to down as a single spring-mass connected

i)$T_1=\pi \sqrt{\frac{m}{k}}$

ii)$k_{eq}=\frac{k.k}{k+k}=\frac{k}{2}$

Now $T_2=\pi \sqrt{\frac{m}{k/2}}$

Total time period $T=T_1+T_2$

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