Physics - SHM Question with Solution | TestHub

The time period of a spring-mass system is given by $T=2\pi \sqrt{\frac{m}{k}}$.

For the initial mass $m$, the time period is $T_1=3$ s:

$3=2\pi \sqrt{\frac{m}{k}}$

When the mass is increased by $0.6$ kg, the new mass is $m+0.6$ and the new time period is $T_2=3+3=6$ s:

$6=2\pi \sqrt{\frac{m+0.6}{k}}$

Dividing the second equation by the first equation, we get:

$\frac{6}{3}=\sqrt{\frac{m+0.6}{m}}$

$2=\sqrt{\frac{m+0.6}{m}}$

Squaring both sides:

$4=\frac{m+0.6}{m}$

$4m=m+0.6$

$3m=0.6$

$m=0.2$ kg

Answer: 0.2 kg