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Question

A spring is made to oscillate after suspending a mass m from one of its ends. The time period obtained is 2 seconds. On increasing the mass by 2 kg, the period of oscillation is increased by 1 second. The initial mass m will be :

A
2 kg
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B
1 kg
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C
0.5 kg
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D
1.6 kg
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Solution

The correct option is D 1.6 kg

We know that ,

T2πmk where T is the time period , m is the initial mass and k is the spring constant .

Thus we can say ,

Tm

2sm -------- (i)

2s+1sm+2

Or 3sm+2 -----------(ii)

Dividing (ii) by (i)

3s2s=Km+2m \\ where K is a constant

Or,(3)2(2)2=m+2m // squaring both sides

Or, 9m=4m+8

Or, 5m=8

Or, m=1.6kg


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