First slide

Damped oscillation

Question

If the differential equation of a damped oscillator is
$\large \frac{{m{d^2}x}}{{d{t^2}}} + \frac{{bdx}}{{dt}} + kx\, = \,0$
then energy of damped oscillator vary with time ‘t’ is E(t) =

Moderate

A

$\large \frac{1}{2}kA_0^2$
B

$\large \frac{1}{2}k{A_o^2}{e^{ - \frac{{bt}}{m}}}$
C

$\large \frac{1}{2}k{A_o^2}{e^{\frac{{bt}}{m}}}$
D

$\large \frac{1}{2}k{A_o^2}{e^{\frac{{bt}}{{2m}}}}$

Solution

Amplitude of a damped harmonic oscillator
$\large A\, = \,{A_o}{e^{\frac{{ - bt}}{{2m}}}}$
$\large \therefore$ Energy of oscillator

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