The amplitude of a damped oscillator decreases to 09 times its original magnitude in 5s In another 10s it will decrease to times its original magnitude where equals physics 2013

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The amplitude of a damped oscillator decreases to 0.9 times its original magnitude in 5s. In another 10s it will decrease to α times its original magnitude, where α equals : - physics 2013

(1) 0.7 (2) 0.81 (3) 0.729 (4) 0.6

By:milan-ransingh

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$A={A}_{0}{e}^{-kt}$
$0.9{A}_{0}={A}_{0}{e}^{-kt}$
$-kt=ln\left(0.9\right)$
$-5k=ln\left(0.9\right)=>-15k=3ln\left(0.9\right)$
$A={A}_{0}{e}^{-15k}={A}_{0}{e}^{-ln\left(0.9{\right)}^{3}}$

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