Two identical springs of spring constant '2k' are attached to a block of mass m and to

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13.Oscillations

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Two identical springs of spring constant $'2k'$ are attached to a block of mass $m$ and to fixed support (see figure). When the mass is displaced from equilibrium position on either side, it executes simple harmonic motion. The time period of oscillations of this sytem is ...... .

A

$2 \pi \sqrt{\frac{ m }{ k }}$

B

$\pi \sqrt{\frac{ m }{2 k }}$

C

$2 \pi \sqrt{\frac{ m }{2 k }}$

D

$\pi \sqrt{\frac{ m }{ k }}$

(JEE MAIN-2021)

Solution

For parallel combination $k _{ eq }= k _{1}+ k _{2}$

$k_{e q}=4 k$

$T =2 \pi \sqrt{\frac{ m }{ k _{ eq }}}$

Standard 11

Physics

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