First slide

Oscillation motion

Question

The oscillation of a body on a smooth horizontal surface is represented by the equation,
$X = A \cos (ω t)$
where x = displacement at time t
$ω$ =frequency of oscillation
Which one of the following graphs shows correctly the variation a with t?

Easy

A
B
C
D

Solution

$Here, X = A \cos ω t$
$∴ Velocity, v = \frac{d X}{d t} = \frac{d}{d t} (A \cos ω t) = - A ω \sin ω t$
$Acceleration, a = \frac{d v}{d t} = \frac{d}{d t} (- A ω \sin ω t) = - A ω^{2} \cos ω t$
$Hence the variation of a with t is correctly shown by graph (c).$

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