First slide

Damped oscillation

Question

If vibrating loaded spring (mass ‘m’) is in a liquid then restoring force (–kx) and viscous force (–bv) are acting. The differential equation for its one dimensional motion is (k = spring constant, b = damping constant)

Easy

A

$\large \frac{{m{d^2}x}}{{d{t^2}}} - bx + \frac{{kdv}}{{dt}}\, = \,0$
B

$\large \frac{{mdx}}{{dt}} - \frac{{b{d^2}x}}{{d{t^2}}} + kx\, = \,0$
C

$\large \frac{{m{d^2}x}}{{d{t^2}}} + \frac{{bdx}}{{dt}} + kx\, = \,0$
D

$\large \frac{{m{d^2}x}}{{d{t^2}}} - \frac{{bdx}}{{dt}} - kx\, = \,0$

Solution

$\large F\, = \, - kx - bv\,\,\, \Rightarrow \,m\frac{{{d^2}x}}{{d{t^2}}} + b\frac{{dx}}{{dt}} + kx\, = \,0$

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