Three masses 700 ,g, 500 ,g, and 400 ,g are s | vedclass

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

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$2 \,s$

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(B) The time period of oscillations for a spring-mass system is given by $T = 2 \pi \sqrt{\frac{m}{k}}$, where $m$ is the oscillating mass and $k$ is the spring constant.Case $I$: When the $700 \,g$ mass is removed, the remaining mass is $m_1 = 500 \,g + 400 \,g = 900 \,g = 0.9 \,kg$. The time period is $T_1 = 3 \,s$.$3 = 2 \pi \sqrt{\frac{0.9}{k}} \quad \dots(i)$Case $II$: When the $500 \,g$ mass is further removed, the remaining mass is $m_2 = 400 \,g = 0.4 \,kg$. Let the new time period be $T_2$.$T_2 = 2 \pi \sqrt{\frac{0.4}{k}} \quad \dots(ii)$Dividing equation $(ii)$ by equation $(i)$:$\frac{T_2}{3} = \frac{2 \pi \sqrt{\frac{0.4}{k}}}{2 \pi \sqrt{\frac{0.9}{k}}} = \sqrt{\frac{0.4}{0.9}} = \sqrt{\frac{4}{9}} = \frac{2}{3}$$T_2 = 3 	imes \frac{2}{3} = 2 \,s$Thus, the system will oscillate with a period of $2 \,s$.

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