Verified Solution • 2025–26 Session moderate

QJEEM23Ph7ae0: JEE Main 2023 Physics - Class 11 JEEM23Ph7ae0 Solution: A mass m attached to free end of a spring executes SHM with a…

A mass m attached to free end of a spring executes SHM with a period of 1s. If the mass is increased by 3 kg the period of the oscillation increases by one second, the value of mass m is ___________ kg.

Step-by-Step Verified Solution

∵2πmk=1\because 2 \pi \sqrt{\frac{m}{k}}=1

Finally

2πm+3k=1+1=22 \pi \sqrt{\frac{m+3}{k}}=1+1=2

Equation (1)(2)\frac{(1)}{(2)} gives

mm+3=12\sqrt{\frac{m}{m+3}}=\frac{1}{2}

∴m=1 kg\therefore m=1 \mathrm{~kg}

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