Q. The amplitude of a damped oscillator becomes half in one minute. The amplitude after $3\ minute$ will be $\frac{1}{X}$ times the original, where $X$ is
A) $2 \times 3$
B) $2^{3}$
C) $3^{2}$
D) $3 \times 2^{2}$
Explanation
(b) Amplitude of damped oscillator
$A = A_{0}e^{- \lambda t};\lambda =$ constant$,\ t =$ time
For$\ t = 1\ min.\frac{A_{0}}{2} = A_{0}e^{- \lambda t} \Rightarrow e^{\lambda} = 2$
For $t = 3$ min. $A = A_{0}e^{- \lambda \times 3} = \frac{A_{0}}{\left( e^{\lambda} \right)^{3}} = \frac{A_{0}}{2^{3}} \Rightarrow X = 2^{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.