In damped oscillations, damping force is directly proportional to…

MCQ

In damped oscillations, damping force is directly proportional to speed of oscillator. If amplitude becomes half of its maximum value in $1 \,s$, then after $2 \,s$ amplitude will be $\left(A_0-\right.$ initial amplitude)

✓
$\frac{1}{4} A_0$
B
$\frac{1}{2} A_0$
C
$A_0$
D
$\frac{\sqrt{3} A_0}{2}$

✓

Answer

Correct option: A.

$\frac{1}{4} A_0$

a
(a)

$A=A_0 e^{-b t}$

Amplitude becomes half hence

$\frac{A_0}{2} A_0 e^{-b t}[t=1]$

$\therefore e^{-b}=\frac{1}{2}$

$\therefore \text { In two seconds }$

$A=A_0\left(\frac{1}{2}\right)^2$

$A=\frac{A_0}{4}$

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