In damped oscillations, the amplitude of oscillations is reduced to one-third of its initial value $a_{0}$ at the end of 100 oscillations. When the oscillator completes 200 oscillations, its amplitude must be

Question

Dr. Abubacker · Accepted Answer

(d) In damped oscillation, amplitude goes on decaying exponentially
$a = a_{0}e^{- bt}$ where $b =$ damping coefficient
Initially, $\frac{a_{0}}{3} = a_{0}e^{- b 	imes 100T},\ T =$ time of one oscillation
or $\frac{1}{3} = e^{- 100bT}$ …(i)
Finally$\ a = a_{0}e^{- b 	imes 200T}\ $or$\ a = a_{0}\left\lbrack e^{- 100bT} ightbrack^{2}$
or $a = a_{0} 	imes \left\lbrack \frac{1}{3} ightbrack^{2}\ $ [From (i)]
or $a = a_{0}/9$

Q. In damped oscillations, the amplitude of oscillations is reduced to one-third of its initial value $a_{0}$ at the end of 100 oscillations. When the oscillator completes 200 oscillations, its amplitude must be

Explanation

Reviewed by Dr. Abubacker

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