Question

In damped vibrations, as time progresses, amplitude of oscillation

• A. decreases
• B. increases
• C. Remains same
• D. Data insufficient

Answer 1

The correct option is A decreases

In damped oscillations, the relation of amplitude of oscillations with time is given by $y=y_o{e}^{-bt}=\frac{y_o}{e^{-bt}}$, where
$y_o=$ initial amplitude of oscillation
$t=$time
$b=$damping constant
since $b>0\&t>0;$
$e^{bt}>1{\Rightarrow e}^{-bt}<1{\Rightarrow y_{o}e}^{-bt}<y_o\Rightarrow y<y_o$
which means that as the time progress, its amplitude will decrease.