A body of mass 600gm is attached to a spring of spring constant k=100N/m and it is performing damped oscillations. If damping constant is 0.2 and driving force is F=F0cos(ωt) where F0=20N, find the amplitude of oscillations at resonance.
A
4.1m
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B
0.57m
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C
7.75m
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D
0.98m
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Solution
The correct option is C7.75m 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=20N m=600g b=0.2rad kg /s Angular frequency of free oscillations ω0=√km=√1000.6=12.9rad/sec Now, we have A=2012.9×0.2=7.75m Thus, option (c) is the correct answer.