Questions

# A particle of mass m is attached to a spring (of spring constant k) and has a natural angular frequency ${\mathrm{\omega }}_{0}$ -An external force F (t) proportional to $\mathrm{cos\omega }\text{\hspace{0.17em}}\mathrm{t}\left(\left(\mathrm{\omega }\ne {\mathrm{\omega }}_{0}\right)$ 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

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detailed solution

Correct option is B

For forced oscillation,x=x0sin(ωt+φ)  and  F=F0cosω twhere,   x0=Fom (ωo2−ω2)∝1m(ωo2−ω2).

The amplitude of vibration of a particle is given by ${\mathrm{a}}_{\mathrm{m}}=\left({\mathrm{a}}_{0}\right)/\left({\mathrm{a\omega }}^{2}-\mathrm{b\omega }+\mathrm{c}\right);$ where ${\mathrm{a}}_{0},\mathrm{a},\mathrm{b}$ and c are positive. The condition for a single resonant frequency is