Question

A simple harmonic motion is represented by $x\left(t\right)=\left(sin\right)^{2} \omega t - 2 \left(cos\right)^{2} ⁡ \omega t$ . The angular frequency of oscillation is given by

• A. $\omega $
• B. $2\omega $
• C. $4\omega $
• D. $\frac{\omega }{2}$

Answer 1

Answer: (B)

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