Question

A block of mass $m$ hangs from three springs having same spring constant $k$. If the mass is slightly displaced downwards, the time period of oscillation will be

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

Answer 1

Answer: (B)

The first two springs are in parallel.
So, $k_{\text {eq }}$ of $1^{\text {st }} 2$ will be $=2 k$
Then it becomes
The springs $2 k$ and $k$ are in series.
So, $ k_{ eq } =\frac{2 k \times k}{2 k+k} $
$=\frac{2 k \times k}{3 k}=\frac{2}{3} k$
$T =2 \pi \sqrt{\frac{m}{k_{e q}}} $
$ \Rightarrow T =2 \pi \sqrt{\frac{3 m}{2 k}}$