First slide

Periodic Motion

Question

The number of harmonic components in the oscillation represented by y - 4 cos² 2t sin 4t and their corresponding angular frequencies are:

Moderate

A

three; 2 rad/s,4 rad/s, 8 rad/s
B

two; 2 rads, 4 rad/s
C

two; 4 rad/s, 8 rad/s
D

two; 2 rad/s, 8 rad/s

Solution

$y = 4 \cos^{2} 2 t \sin 4 t = 2 (1 + \cos 4 t) \sin 4 t = 2 \sin 4 t + 2 \sin 4 t \cos 4 t = 2 \sin 4 t + \sin 8 t$
Number of harmonic components = 2
$ω = 4 ras / s, 8 rad / s .$

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