Question

Which of the following expressions does not represent simple harmonic motion?

• A. $x=A cos \omega t +B sin \omega t$
• B. $x=A cos \left(\omega t+\alpha\right)$
• C. $x=B sin \left(\omega t+\beta\right)$
• D. $x=A sin \omega t \,cos^{2}\omega t$

Answer 1

Answer: (D)

$x=A sin \omega t \,cos^{2}\omega t$

Answer 2

Simple harmonic motion is represented by a sine function or a cosine function or a linear combination of both. Hence, options $(a), (b)$ and $(c)$ represent simple harmonic motion while option $(d)$ is a product of the two functions (sine and cosine) does not represent a simple harmonic motion.