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)

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