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  4. A simple harmonic motion is represented by x(t) = sin2 ω t - 2 cos2 ω t . The angular frequency of oscillation is given by

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Q. A simple harmonic motion is represented by $x(t) = \sin^2 \omega t - 2 \, \cos^2 \, \omega t$ . The angular frequency of oscillation is given by

KEAMKEAM 2017Oscillations

Solution:

$x=\sin ^{2} \omega t -2 \cos ^{2} \omega t $
$=1-3 \cos ^{2} \omega t $
$=1-3\left(\frac{1+\cos 2 \omega t}{2}\right) $
$=-\frac{1}{2}-\frac{3}{2} \cos \,2 \,\omega t$
which is a periodic function with angular frequency of $2\, \omega$.