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

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

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

JEE MainJEE Main 2023Oscillations

Solution:

$ T =2 \pi \sqrt{\frac{ m }{ k }}=1$
$T ^{\prime}=2 \pi \sqrt{\frac{ m +3}{ k }}=2 $
$ \frac{ T }{ T ^{\prime}}=\sqrt{\frac{ m }{ m +3}}=\frac{1}{2}$
$ \Rightarrow \frac{ m }{ m +3}=\frac{1}{4} $
$ m =1$