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Q.

A particle of mass m is attached to a spring (of spring constant k) and has a natural angular frequency ω0. An extemal force F(t) proportional to cos ω t(ω ≠ w0) is applied to the oscillator. The time displacement of the oscillator will be proportional to

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a

mω02-ω2

b

1m(ω02-ω2)

c

1m(ω12+ω2)

d

mω12+ω2

answer is B.

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Detailed Solution

For forced oscillation,x = x0sin(ωt+φ)  and F = F0cos ωtwhere, x0 = F0m(ω02-ω2) α 1m(ω02-ω2)
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A particle of mass m is attached to a spring (of spring constant k) and has a natural angular frequency ω0. An extemal force F(t) proportional to cos ω t(ω ≠ w0) is applied to the oscillator. The time displacement of the oscillator will be proportional to