Question

The amplitude of a damped oscillator becomes $\left(\frac{1}{3}\right)rd$ in $2$ seconds. If its amplitude after $6$ seconds is $\frac{1}{n}$ times the original amplitude, the value of $n$ is

• A. $3^2$
• B. $3^3$
• C. $3 \sqrt{2}$
• D. $2^3$

Answer 1

Answer: (B)

$3^3$

Answer 2

Let original amplitude $= A$
Amplitude after $2\, \sec =\frac{ A }{3}$
Amplitude after next $2\, \sec =\frac{ A }{3} \times \frac{1}{3}=\frac{ A }{9}$
Amplitude again after $2\, \sec =\frac{1}{3} \times \frac{ A }{9}$
$=\frac{ A }{27}=\frac{ A }{3^{3}}$
Here $n=3^{3}$