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Solve it, - Oscillations and Waves - JEE Main-3

The equation of a damped SHM is given by m\frac{d^{2}x}{dt^{2}} + b \frac{dx}{dt} + kx =0, then angular frequency will be

  • Option 1)

    \omega =[ \frac{k}{m}- \frac{b^{2}}{4m^{2}}]^{\frac{1}{2}}

  • Option 2)

    \omega =[ \frac{k}{m}- \frac{b}{4m}]^{\frac{1}{2}}

  • Option 3)

    \omega =[ \frac{k}{m}- \frac{b^{2}}{4m}]^{\frac{1}{2}}

  • Option 4)

    \omega =[ \frac{k}{m}- \frac{b^{2}}{4m^{2}}]

 
Answers (1)
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Equate with standard equation of SHM

\frac{d^{2}}{dt^{2}} = -\omega^{2} t

 

Damped Harmonic motion -

equation of motion

m\frac{du}{dt}= -Kx-bu
  

- wherein

  -bu is restitute

-Kx is restoring force

 

 

 


Option 1)

\omega =[ \frac{k}{m}- \frac{b^{2}}{4m^{2}}]^{\frac{1}{2}}

This is correct.

Option 2)

\omega =[ \frac{k}{m}- \frac{b}{4m}]^{\frac{1}{2}}

This is incorrect.

Option 3)

\omega =[ \frac{k}{m}- \frac{b^{2}}{4m}]^{\frac{1}{2}}

This is incorrect.

Option 4)

\omega =[ \frac{k}{m}- \frac{b^{2}}{4m^{2}}]

This is incorrect.

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