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A particle of mass (m) is attached to a spring (of spring constant k) and has a narural angular frequency omega_(0). An external force `R(t)` proportional to cos omegat(omega!=omega)(0) is applied to the oscillator. The time displacement of the oscillator will be proprtional to. |
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Answer» Given the natureal angular frequency `=omega_(0)`. If the displacement of the particle is y, then acceleration of the particle is, `a_(0)=-omega_(0)^(2)y` The external force `F(t)propcosomegat.` It has an angular frequency `omega`. For the displacement y, the acceleration produced by this force is `a_(1)=omega^(2)y` Net acceleration of the particle at displacement y is `a=a_(0)+a_(1)=-omega_(0)^(2)y+omega^(2)y=-(omega_(0)^(2)-omega^(2))y` Net force on the particle at displacement y is `F=ma=-m(omega_(0)^(2)-omega^(2))y` or `y=(F)/(m(omega_(0)^(2)-omega^(2)))` So`yprop (1)/(m(omega_(0)^(2)-omega^(2)))` |
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