Question

The function sin wt – cos wt 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)

A simple harmonic motion with a period $\frac{2\pi}{\omega}$

Answer 2

$\sin\omega t - \cos\varepsilon t = \sqrt{2}\left( \frac{1}{\sqrt{2}}\sin\omega t - \frac{1}{\sqrt{2}}\cos\omega t \right)$

$= \sqrt{2}\left( \sin\omega t\cos\frac{\pi}{4} - \cos\omega t\sin\frac{\pi}{4} \right)$

$= \sqrt{2}\sin\left( \omega t - \frac{\pi}{4} \right)$

It represents SHM with a period $\frac{2\pi}{\omega}$