Q

# 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)

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

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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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