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Question

A weakly damped harmonic oscillator is executing resonant oscillations. The phase difference between the oscillator and the external periodic force is:

A
Zero
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B
π/4
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C
π/2
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D
π
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Solution

The correct option is C π/2
The equation for forced oscillation in a damped system is given as-
md2xdt2+bdxdt+kx=F0cosωt
Dividing by m throughout,
d2xdt2+2βdxdt+ω20x=Acosωt
The expected solution is of form x=Dcos(ωtδ)
Put this is in above equation gives,
tanδ=2βωω20ω2
For resonant oscillation, ω0=ω
δ=π/2 which is the phase difference between x and F.

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