Question

The function $sin \omega t- cos \omega t $ represents

• A. a simple harmonic motion with a period $\frac{\pi}{\omega}$
• B. a simple harmonic motion with a period $\frac{2\pi}{\omega}$
• C. a periodic, but not simple harmonic motion with a period $\frac{\pi}{\omega}$
• D. a periodic, but not simple harmonic motion with a period $\frac{2\pi}{\omega}$

Answer 1

Answer: (B)

$sin \,\omega t -cos\, \omega t = \sqrt{2}\left(\frac{1}{\sqrt{2}} sin \,\omega t -\frac{1}{\sqrt{2}} cos\, \omega t\right) $
$= \sqrt{2} \left(sin\, \omega t\,cos \,\frac{\pi}{4} - cos \,\omega t \,sin \frac{\pi}{4}\right) = \sqrt{2} sin \left(\omega t -\frac{\pi}{4}\right)$
It represents $SHM$ with a period $ \frac{2\pi}{\omega}$