### 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 $

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

$\frac{T}{T^{\prime}}=\sqrt{\frac{m}{m+3}}=\frac{1}{2}$

$\Rightarrow \frac{m}{m+3}=\frac{1}{4}$

$m=1$