A mass 'm' attached to a spring oscillates wi | vedclass

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(B) The time period of a mass-spring system is given by $T = 2 \pi \sqrt{\frac{m}{k}}$.For the initial mass $m$,the period $T_1 = 3 \ s$:$3 = 2 \pi \s

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$0.2$

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(B) The time period of a mass-spring system is given by $T = 2 \pi \sqrt{\frac{m}{k}}$.For the initial mass $m$,the period $T_1 = 3 \ s$:$3 = 2 \pi \sqrt{\frac{m}{k}} \implies \frac{9}{4 \pi^2} = \frac{m}{k} \implies k = \frac{4 \pi^2 m}{9} \quad \dots (i)$When the mass is increased by $0.6 \ kg$,the new mass is $m' = m + 0.6$ and the new period $T_2 = 3 + 3 = 6 \ s$:$6 = 2 \pi \sqrt{\frac{m + 0.6}{k}} \implies 3 = \pi \sqrt{\frac{m + 0.6}{k}} \implies 9 = \pi^2 \frac{m + 0.6}{k} \implies \frac{9}{\pi^2} = \frac{m + 0.6}{k} \quad \dots (ii)$Dividing equation $(ii)$ by equation $(i)$:$\frac{9 / \pi^2}{9 / 4 \pi^2} = \frac{(m + 0.6) / k}{m / k}$$4 = \frac{m + 0.6}{m}$$4m = m + 0.6$$3m = 0.6$$m = 0.2 \ kg$.

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

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