Question

Which of the following functions represents a simple harmonic oscillation?

• A. $sin\omega t-cos\omega t$
• B. $si{n}^2\omega t$
• C. $sin\omega t+sin2\omega t$
• D. $sin\omega t-sin2\omega t$

Answer 1

The correct option is A $sin\omega t-cos\omega t$

$sin\omega t-cos\omega t=\sqrt{2}[\frac{1}{\sqrt{2}}sin\omega t-\frac{1}{\sqrt{2}}cos\omega t]$
$=\sqrt{2}[cos\frac{\pi }{4}.sin\omega t-sin\frac{\pi }{4}cos\omega t]$
$=\sqrt{2}sin(\omega t-\pi /4)$ [which represents simple harmonic motion]