Three blocks of masses 700 ,g,500 ,g,and 400 | vedclass

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(B) The period of oscillation for a spring-mass system is given by $T = 2 \pi \sqrt{\frac{m}{k}}$,where $m$ is the total mass and $k$ is the spring co

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$2 \,s$

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(B) The period of oscillation for a spring-mass system is given by $T = 2 \pi \sqrt{\frac{m}{k}}$,where $m$ is the total mass and $k$ is the spring constant.Case $1$: When the $700 \,g$ block is removed,the remaining mass is $m_1 = (500 + 400) \,g = 900 \,g = 0.9 \,kg$.The period is $T_1 = 3 \,s$.So,$3 = 2 \pi \sqrt{\frac{0.9}{k}}$.Squaring both sides: $9 = 4 \pi^2 \left( \frac{0.9}{k} ight) \Rightarrow k = \frac{4 \pi^2 	imes 0.9}{9} = 0.4 \pi^2 \,N/m$.Case $2$: When both $700 \,g$ and $500 \,g$ blocks are removed,the remaining mass is $m_2 = 400 \,g = 0.4 \,kg$.The new period $T_2$ is given by:$T_2 = 2 \pi \sqrt{\frac{m_2}{k}} = 2 \pi \sqrt{\frac{0.4}{0.4 \pi^2}}$.$T_2 = 2 \pi \sqrt{\frac{1}{\pi^2}} = 2 \pi \left( \frac{1}{\pi} ight) = 2 \,s$.

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