First slide

Damped oscillation

Question

If the differential equation of a damped oscillator is $\large \frac{{m{d^2}x}}{{d{t^2}}} + \frac{{bdx}}{{dt}} + kx\, = \,0$ then for small damping $\large \frac{b}{{\sqrt {km} }}$ is

Moderate

A

= 1
B

< 2
C

> 1
D

$\large > / < 1$

Solution

For small damping, motional of the block becomes oscillatory. For this the condition (b² -4km) < 0 must be satsified.
$\large \therefore \,\frac{b}{{\sqrt {km} }}\, < \,2$ must be satisfied.

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