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  4. 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 system is: <img class=img-fluid question-image alt=image src=https://cdn.tardigrade.in/img/question/physics/9337a87e2484a799b8aa1c380656caa0-.png />

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Q. 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 system is :

image

JEE MainJEE Main 2021Oscillations

Solution:

For parallel combination $k _{ eq }= k _{1}+ k _{2}$
$k _{ eq }=4 k$
$T =2 \pi \sqrt{\frac{ m }{ k _{ eq }}}$