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In forced oscillation of a particle the amplitude is maximum for a frequency \omega _{1}  of the force, while the energy is maximum for a frequency \omega _{2} of the force, then

  • Option 1)

    \omega _{1}= \omega _{2}

  • Option 2)

    \omega _{1}> \omega _{2}

  • Option 3)

    \omega _{1}< \omega _{2}  when damping is small and  \omega _{1}> \omega _{2}  when damping is large 

  • Option 4)

    \omega _{1}< \omega _{2}

 

Answers (1)

best_answer

(i) The amplitude is maximum at resonance

\therefore\: Natural \: frequency\: = Frequency\: of \: force\: = \omega _{1}

(ii) The energy is maximum at resonance

\therefore\: Natural \: frequency\: = Frequency\: of \: force\: = \omega _{2}

\therefore\: from\: (i)\: and \: (ii),

\omega _{1}= \omega _{2}


Option 1)

\omega _{1}= \omega _{2}

This option is correct.

Option 2)

\omega _{1}> \omega _{2}

This option is incorrect.

Option 3)

\omega _{1}< \omega _{2}  when damping is small and  \omega _{1}> \omega _{2}  when damping is large 

This option is incorrect.

Option 4)

\omega _{1}< \omega _{2}

This option is incorrect.

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