Question 252: Oscillations

Question

If the period of a oscillation of mass ' m ' suspended from a spring is 2 s , then the period of suspended mass ' 4 m ' with the same spring will be

Accepted Answer

The time period $T$ of a mass-spring system is given by:
$ T = 2\pi \sqrt{\frac{m}{k}} $
where
$m =$ mass suspended from the spring
$k =$ spring constant
Given:
For $m$, $T_1 = 2$ s
Now, for mass $4m$, the new period $T_2$ will be:
$ T_2 = 2\pi \sqrt{\frac{4m}{k}} $
$ = 2\pi \sqrt{4} \sqrt{\frac{m}{k}} $
$ = 2\pi 	imes 2 \sqrt{\frac{m}{k}} $
$ = 2 	imes \left(2\pi \sqrt{\frac{m}{k}}ight) $
But $2\pi \sqrt{\frac{m}{k}} = T_1 = 2$ s
So,
$ T_2 = 2 	imes 2 = 4~	ext{s} $
Answer: Option D (4 s)

Answer

1 s

Answer

3 s

Answer

2 s

Answer

4 s

Oscillations

If the period of a oscillation of mass ' m ' suspended from a spring is 2 s , then the period of suspended mass ' 4 m ' with the same spring will be

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