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  • Stuck here, help me understand: - Oscillations and Waves - JEE Main-5

The amplitude of vibration of a particle is given by a_{m } =\frac{a_{o}}{a\omega^{2} - b\omega + c} where a_{o}, a, b and c are positive. The condition for a single resultant frequency is 

  • Option 1)

    b^{2} = 4ac

  • Option 2)

    b^{2} > 4ac

  • Option 3)

    b^{2} = 5ac

  • Option 4)

    b^{2} = 7ac

 

Answers (1)

best_answer

For resonance amplitude must be maximum which is possible onlt when the denominator of the explansion is zero

i.e. a\omega^{2} - b\omega + c = 0 \Rightarrow \omega = \frac{+b\pm \sqrt{b^{2 - 4ac}}}{2a}

for a single resonant frequency, b^{2} = 4ac

 

Amplitude in forced oscillation -

A= \frac{F_{0}/m}{\sqrt{\left ( \omega ^{2}-\omega {_{0}}^{2} \right )^{2}+\left ( \frac{b\omega }{m} \right )^{2}}}

 

- wherein

\omega _{0}= \sqrt{K/m}

is caused natural angular frequency

 

 

 


Option 1)

b^{2} = 4ac

This is correct.

Option 2)

b^{2} > 4ac

This is incorrect.

Option 3)

b^{2} = 5ac

This is incorrect.

Option 4)

b^{2} = 7ac

This is incorrect.

Posted by

Plabita

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