Q. Two identical springs are connected to mass $m$ as shown $(k = spring\ constant)$. If the period of the configuration in (a) is 2 s, the period of the configuration in (b) is
A) $2\sqrt{2}$ s
B) $1$ s
C) $\frac{1}{\sqrt{2}}$ s
D) $\sqrt{2}$ s
Explanation
(b) Time period $T = 2\pi\sqrt{\frac{m}{k}}$
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$\therefore$ $\frac{T_{1}}{T_{2}} = \sqrt{\frac{k_{2}}{k_{1}}}$
$\frac{2}{T} = \sqrt{\frac{2k}{\frac{k}{2}}} = 2$
$T = 1$ s
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.