Question

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

• A. $x=Acos\omega t+Bsin\omega t$
• B. $F=\sqrt{ky}$
• C. $F=ky$
• D. none of these

Answer 1

Answer: (A)

$x=Acos\omega t+Bsin\omega t$

For an equation to represent SHM, it must satisfy $\frac{d^{2}x}{d{t}^2}=-kx$

Considering option (A)

$\frac{d^2(Acos\omega t+Bsin\omega t)}{d{t}^2}\ne -k(Acos\omega t+Bsin\omega t)$

So the expression $x=Acos\omega t+Bsin\omega t$ does not represent simple harmonic motion.