Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa

A particle with restoring force propotional to displacement and resisting force propotional to velocity is subjected to a force F = \sin\omega t. If the amplitude of the particle is maximum for \omega = \omega_{1} and the energy is of the particle is maximum for \omega = \omega_{2} then (where \omega_{o} is natural frequency of oscillation of particle.)

  • Option 1)

    \omega_{1} = \omega_{o}\; and\;\; \omega_{2} \neq \omega_{o}

  • Option 2)

    \omega_{1} = \omega_{o}\; and\;\; \omega_{2} = \omega_{o}

  • Option 3)

    \omega_{1} \neq \omega_{o}\; and\;\; \omega_{2} = \omega_{o}

  • Option 4)

    \omega_{1} \neq \omega_{o}\; and\;\; \omega_{2} \neq \omega_{o}

 

Answers (1)

best_answer

Energy of particle is maximum at resonant frequency i.e \omega_{2} = \omega_{0}. For amplitude resonance (amplitude maximum) frequency of driver force

\omega = \sqrt{\omega_{0}^{2} -(\frac{b}{2m})^{2}} \Rightarrow \omega_{1} \neq \omega_{0}

 

Resonance -

If we vary the angular frequency \omega of the applied force,this amplitude changes and becomes maximum.

\omega = \omega '= \sqrt{\omega {_{0}}^{2}-\frac{b^{2}}{4m^{2}}}

- wherein

When this condition is fulfilled it is caused resonance.

 

 

 


Option 1)

\omega_{1} = \omega_{o}\; and\;\; \omega_{2} \neq \omega_{o}

This is incorrect.

Option 2)

\omega_{1} = \omega_{o}\; and\;\; \omega_{2} = \omega_{o}

This is incorrect.

Option 3)

\omega_{1} \neq \omega_{o}\; and\;\; \omega_{2} = \omega_{o}

This is correct.

Option 4)

\omega_{1} \neq \omega_{o}\; and\;\; \omega_{2} \neq \omega_{o}

This is incorrect.

Posted by

Avinash

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2024 session 2 result date announced; Steps to check NTA session 2 scores
anam-khan

JEE Main 2024 session 2 final answer key soon at jeemain.nta.ac.in; result on April 25
anam-khan

JEE Main 2024 Session 2: Last day to challenge answer key today

Latest Question