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A particle of mass m is attached to a spring and has natural angular frequency  \omega_{o}. An external force  F(t)propotional to \cos\omega t\;\; (\omega \neq \omega_{o}) is applied to the oscillator. The displacement of the oscillator will be propotional to 

  • Option 1)

    \frac{m}{\omega_{0}^{2} - \omega^{2}}

  • Option 2)

    \frac{1}{m(\omega_{0}^{2} - \omega^{2})}

  • Option 3)

    \frac{1}{m(\omega_{0}^{2} + \omega^{2})}

  • Option 4)

    \frac{m}{(\omega_{0}^{2} + \omega^{2})}

 

Answers (1)

best_answer

For forced oscillation,

x_{o} = \frac{F_{0}}{m(\omega^{2}_{0}- \omega^{2})}\;\alpha\; \frac{1}{m(\omega^{2}_{0}- \omega^{2})}

 

Forced Oscillation -

In certain situation apart from the restoring force and the damping force, there is yet another force which changes periodically.

 

- wherein

m\frac{du}{dt}= -kx-bu+f_{0}\sin \omega t

 

 

 


Option 1)

\frac{m}{\omega_{0}^{2} - \omega^{2}}

This is incorrect.

Option 2)

\frac{1}{m(\omega_{0}^{2} - \omega^{2})}

This is correct.

Option 3)

\frac{1}{m(\omega_{0}^{2} + \omega^{2})}

This is incorrect.

Option 4)

\frac{m}{(\omega_{0}^{2} + \omega^{2})}

This is incorrect.

Posted by

prateek

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