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Free, damped and forced oscillations - class-XI
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$mx^{2} - bx + k = 0$. Find time after which to the energy will become half of initial maximum value in damped forced oscillation.
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A
$t = \dfrac {m}{b} \times \dfrac {1}{2} ln2$
💡 Explanation:
$\dfrac {1}{\sqrt {2}} = e^{-bt/m}$
$ln \sqrt {2} = \dfrac {bt}{m}$
$t = \dfrac {m}{b} \times \dfrac {1}{2} ln2$.