Oscillations Question 3
Question 3 - 24 January - Shift 2
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.
Show Answer
Answer: (1)
Solution:
Formula: Time period of spring mass system
$ T=2 \pi \sqrt{\frac{m}{k}}=1 $
$T^{\prime}=2 \pi \sqrt{\frac{m+3}{k}}=2$
$\frac{T}{T^{\prime}}=\sqrt{\frac{m}{m+3}}=\frac{1}{2}$
$\Rightarrow \frac{m}{m+3}=\frac{1}{4}$
$m=1$
