Three masses 700 , g, 500 , g,and 400 , g are | 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 oscillating mass and $k$ is the spri

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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 oscillating mass and $k$ is the spring constant.Case $1$: When the $700 \, g$ mass is removed,the remaining mass is $m_1 = 500 \, g + 400 \, g = 900 \, g$. The period is $T_1 = 3 \, s$.$3 = 2\pi \sqrt{\frac{900}{k}} \quad \dots (i)$Case $2$: When the $500 \, g$ mass is also removed,the remaining mass is $m_2 = 400 \, g$. Let the new period be $T_2$.$T_2 = 2\pi \sqrt{\frac{400}{k}} \quad \dots (ii)$Dividing equation $(i)$ by equation $(ii)$:$\frac{3}{T_2} = \frac{2\pi \sqrt{\frac{900}{k}}}{2\pi \sqrt{\frac{400}{k}}} = \sqrt{\frac{900}{400}} = \sqrt{\frac{9}{4}} = \frac{3}{2}$Therefore,$T_2 = 2 \, s$.

Three masses $700 \, g, 500 \, g$,and $400 \, g$ are suspended at the end of a spring as shown and are in equilibrium. When the $700 \, g$ mass is removed,the system oscillates with a period of $3 \, s$. When the $500 \, g$ mass is also removed,it will oscillate with a period of ...... $s$.

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