Two identical springs of spring|SIMPLE HARMONIC MOTION|JEE-Main 2021

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JEE MAIN 2021

25-02-2021 S2

Question

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 :

Select the correct option:

A

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

B

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

C

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

D

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

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

For parallel combination $\mathrm{k}_{\mathrm{eq}}=\mathrm{k}_1+\mathrm{k}_2$ $$ \begin{aligned} \mathrm{k}_{\mathrm{eq}} & =4 \mathrm{k} \\ \mathrm{~T} & =2 \pi \sqrt{\frac{\mathrm{~m}}{\mathrm{k}_{\mathrm{eq}}}} \end{aligned} $$

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