Question

A particle is performing damped oscillation with frequency $5Hz$. After every $10$ oscillations its amplitude becomes half. find time from beginning after which the amplitude becomes $\frac{1}{1000}$ of its initial amplitude:

• A. $10s$
• B. $20s$
• C. $25s$
• D. $50s$

Answer 1

The correct option is B $20s$

$f=5$
so $T=\frac{1}{5}$
$10T=\frac{10}{5}=2$
$\frac{A_0}{1000}=A_0{\left(\frac{1}{2}\right)}^{t/2}$
$(2{)}^{t/2}=1000$
$\left(\frac{t}{2}\right)log2=3$
$t=\frac{6}{log2}\approx 20s$