Question

Which of the following equation does not represent a SHM?

• A. $\cos \omega t+\sin \omega t$
• B. $\sin \omega t-\cos \omega t$
• C. $1-\sin 2\omega t$
• D. $\sin \omega t+\cos (\omega t+\alpha )$

Answer 1

The correct option is C $1-\sin 2\omega t$

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

Consider option C,

$x=1-sin2\omega t$

$\Rightarrow \frac{d^{2}x}{d{t}^2}=4sin2\omega t$

which cannot be expressed as $c(1-sin2\omega t)$

where $c$ is a constant.

Hence this does not represent an SHM.