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Question

A body of mass 600 gm is attached to a spring of spring constant k=100 N/m and it is performing damped oscillations. If damping constant is 0.2 and driving force is F=F0cos(ωt) where F0=20 N, find the amplitude of oscillations at resonance.

A
4.1 m
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B
0.57 m
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C
7.75 m
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D
0.98 m
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Solution

The correct option is C 7.75 m
We know that, amplitude of oscillation at resonance is given by
A=F02mγω0=F0bω0
where b is the damping constant.
From the data given in the question,
F0=20 N
m=600 g
b=0.2 rad kg /s
Angular frequency of free oscillations
ω0=km=1000.6=12.9 rad/sec
Now, we have
A=2012.9×0.2=7.75 m
Thus, option (c) is the correct answer.

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