First slide

Damped oscillation

Question

If the differential equation of a damped oscillator is $\large m\frac{{{d^2}x}}{{d{t^2}}} + b\frac{{dx}}{{dt}} + kx\, = \,0$ then its amplitude A₀ vary with time ‘t’ as A₀(t) =

Easy

A

$\large A{e^{\frac{{bt}}{{2m}}}}$
B

$\large A{e^{\frac{{ - bt}}{m}}}$
C

$\large A{e^{\frac{{bt}}{m}}}$
D

$\large A{e^{\frac{{ - bt}}{{2m}}}}$

Solution

Displacement equation for damping motion is $\large y\, = \,A.{e^{\frac{{ - bt}}{{2m}}}},\operatorname{Cos} \left( {{w^1}t + \phi } \right)$ Anptitude $\large A.{e^{ - \frac{b}{{2m}}.t}}$

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