$m x^{2}-b x+k=0$
Find time after which to the energy will become half of initial maximum value in damped force oscillation.
AIIMS 2019, Diffcult
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The time after which the energy will become half of initial maximum value in damped forced oscillation is calculated as,
$\frac{1}{\sqrt{2}}=e^{-b t / m}$
$\ln \sqrt{2}=\frac{b t}{m}$
$t=\frac{m}{b} \times \frac{1}{2} \ln 2$
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