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13.Oscillations
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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
$2 \pi \sqrt{\frac{3 k}{m}}$
Solution
(b)
The first two springs are in parallel.
So, $k_{ eq }$ of $1^{\text {st }} 2$ will be $=2 k$
Then it becomes
The springs $2 k$ and $k$ are in series.
$\text { So, }$ $k_{ eq }=\frac{2 k \times k}{2 k+k}$
$=\frac{2 k \times k}{3 k}=\frac{2}{3} k$
$T=2 \pi \sqrt{\frac{m}{k_{e q}}}$
$\Rightarrow T=2 \pi \sqrt{\frac{3 m}{2 k}}$
Standard 11
Physics
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