Question

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

• A. $\omega$
• B. $2 \, \omega$
• C. $4 \, \omega$
• D. $\omega / 2$

Answer 1

Answer: (B)

$2 \, \omega$

Answer 2

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