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The system shown in figure can oscillate on smooth surface. Masses are of 3 kg and 6 kg and the spring constant is 800 N/m. The spring is initially compressed by 6 cm and released. The time period of vibration is

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$\frac{2 π}{5} s$

$\frac{π}{20} s$

$\frac{π}{10} s$

$\frac{π}{5} s$

answer is A.

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Detailed Solution

$T = 2 π \sqrt{\frac{m}{k}} = 2 π \sqrt{\frac{2}{800}} = \frac{π}{10} s$

effective reduced mass= $\frac{m_{1} m_{2}}{m_{1} + m_{2}} = m = 2 k g$

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