JEE Main · 2013 · 07 Apr 2013 · Offline · Elasticity & SHM

The amplitude of a damped oscillator decreases to 0.9 times its original magnitude is 5 s . In another 10 s it will decrease to

α

times its original magnitude, where

α

equals.

Answer: (B)

Solution

A damped amplitude decays exponentially,

A = A_{0} e^{- k t}

. The first

5 s

bring it to

0.9 A_{0}

, so

e^{- 5 k} = 0.9

. After a further

10 s

, three such intervals in all, the factor is

e^{- 15 k} = (e^{- 5 k})^{3} = (0.9)^{3} = 0.729

, so the amplitude then stands at

0.729 A_{0}

JEE Main · 2013 · 07 Apr 2013 · Offline · Single correct option