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Question

A spring stretches by 0.05 m when a mass of 0.5 kg is hung from it. A body of mass 1.0 kg is attached to one of its ends, the other end being fixed to the wall. The body is pulled 0.01 m along a horizontal frictionless surface and released. What is the total energy of the oscillator. Assume the string to have negligible mass and take g=10ms2

A
0.005 J
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B
0.05 J
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C
0.5 J
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D
5 J
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Solution

The correct option is A 0.005 J
Force acting on spring = mg = 0.5 × 10 = 5N. This force extends the spring by 0.05 m. Therefore, the force constant is
k=50.05=100Nm1
The angular frequency of horizontal oscillations is
ω=km=1001.0 rad s1
The amplitude is A = 0.01 m. Therefore, total energy is
E=12mA2ω2=12×1.0×(0.01)2×(10)2=0.005J
Hence the correct choice is (a).

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