Masses m and 3m are attached to the two ends of a spring of spring constant k. The period of oscillation is _______.

2 π \sqrt{k / m}

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4 π \sqrt{m / k}

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π \sqrt{3 m / k}

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π \sqrt{3 m / 2 k}

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Solution

The correct option is C $π \sqrt{3 m / k}$
The time period of oscillation of the system is given by: $T^{'} = 2 π \sqrt{\frac{μ}{k}}$ .
Where $μ$ = reduced mass of the system $= \frac{m_{1} m_{2}}{m_{1} + m_{2}} = \frac{m .3 m}{m + 3 m} = \frac{3 m}{4}$
$k$ =Spring constant.
So, $T = 2 π \sqrt{\frac{3 m}{4 k}} = π \sqrt{\frac{3 m}{k}}$

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Masses m and 3m are attached to the two ends of a spring of spring constant k. The period of oscillation is _______.

The correct option is C π√3m/kThe time period of oscillation of the system is given by: T′=2π√μk.Where μ= reduced mass of the system=m1m2m1+m2=m.3mm+3m=3m4k=Spring constant.So, T=2π√3m4k=π√3mk