Q. The amplitude of damped oscillator becomes $\frac{1}{2}$ in 2 s. Its amplitude after 6 is 1/$n$ times the original. Then $n$ is equal to
A) $2^{3}$
B) $3^{2}$
C) $3^{\frac{1}{3}}$
D) $3^{3}$
Explanation
(d) For damped motion $a = a_{0}e^{- bt}$
For first case,
$\frac{a_{0}}{3} = a_{0}e^{- b \times 2}\ or\frac{1}{3} = e^{- 2b}$
For second case,
$\frac{a_{0}}{n} = a_{0}e^{- b \times 6}\ or\frac{1}{n} = e^{- 6b} = \left( e^{- 2b} \right)^{3} = \left( \frac{1}{3} \right)^{3}\ n = 3^{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.