A mass ' $m$ ' attached to a spring oscillates with a period of 3 second. If the mass is increased by 0.6 kg , the period increases by 3 second. The initial mass ' m ' is equal to

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Aicharya · Accepted Answer

Time period, $\begin{array}{rlrl} & & \mathrm{T} & =2 \pi \sqrt{\frac{\mathrm{~m}}{\mathrm{k}}} \\ & \therefore \quad \mathrm{~T}_1 & =2 \pi \sqrt{\frac{\mathrm{~m}}{\mathrm{k}}} \\ & \therefore \quad 3 & =2 \pi \sqrt{\frac{\mathrm{~m}}{\mathrm{k}}} \\ & \frac{9}{4 \pi^2} & =\frac{\mathrm{m}}{\mathrm{k}} \\ & \therefore \quad \mathrm{k} & =\frac{4 \pi^2 \mathrm{~m}}{9} \end{array}$ ...(given, $\mathrm{T}_1=3 \mathrm{~s}$ )
When mass is increased by 0.6 kg , $\mathrm{T}_2=2 \pi \sqrt{\frac{\mathrm{~m}+0.6}{\mathrm{k}}}$ ...[From(i)] $6=\sqrt{\frac{m+0.6}{k}}$. ... (given $\mathrm{T}_2=3+3=6 \mathrm{~s}$ ) $\frac{36}{4 \pi^2}=\frac{m+0.6}{k}$ $\begin{aligned} & \frac{36}{4 \pi^2}=(\mathrm{m}+0.6) \frac{9}{4 \pi^2 \mathrm{~m}} \\ & 4 \mathrm{~m}=\mathrm{m}+0.6 \\ & \mathrm{~m}=0.2 \mathrm{~kg}\end{aligned}$

A mass ' $m$ ' attached to a spring oscillates with a period of 3 second. If the mass is increased by 0.6 kg…

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