Question

In damped oscillations, the amplitude after $50$ oscillations is $0.8a_0$, where $a_0$ is the initial amplitude, then the amplitude after $150$ oscillations is

• A. $0.512a_0$
• B. $0.280a_0$
• C. Zero
• D. $a_0$

Answer 1

Answer: (A)

$0.512a_0$

The amplitude, a, at time $t$ is given by $a=a_{0}exp(-\alpha t)$

$a_{50}=a_{0}exp(-\alpha \times 50T)=0.80a_0$

where $T$ is the period of oscillation

$a_{150}=a_{0}exp(-a\times 150T)$

$=a_0(0.8{)}^3=0.512a_0$