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QJEEM23Ph417d: JEE Main 2023 Physics - Class 11 JEEM23Ph417d Solution: A block of a mass 2 kg is attached with two identical springs…

JEE Main 2023 (Online) 24th January Morning Shift Physics - Simple Harmonic Motion Question 34 English

A block of a mass 2 kg is attached with two identical springs of spring constant 20 N/m each. The block is placed on a frictionless surface and the ends of the springs are attached to rigid supports (see figure). When the mass is displaced from its equilibrium position, it executes a simple harmonic motion. The time period of oscillation is πx\frac{\pi}{\sqrt x} in SI unit. The value of xx is ____________.

Step-by-Step Verified Solution

Both the springs are in parallel so net spring constant is Knet =K1+K2=40 N/mK_{\text {net }}=K_{1}+K_{2}=40 \mathrm{~N} / \mathrm{m}

So T=2πmKnetT=2 \pi \sqrt{\frac{m}{K_{n e t}}}

amp;=2π240amp;=π5\begin{aligned}& =2 \pi \sqrt{\frac{2}{40}} \\\\& =\frac{\pi}{\sqrt{5}}\end{aligned}

∴x=5\therefore x=5

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