Which one of the following equations of motion represents simple harmonic motion? (Where $k, k_0, k_1$ and $a$ are all positive constants)

Which of the following functions of time represent $(a)$ periodic and $(b)$ non-periodic motion? Give the period for each case of periodic motion $[\omega$ is any positive constant].
$(i)$ $\sin \omega t + \cos \omega t$
$(ii)$ $\sin \omega t + \cos 2\omega t + \sin 4\omega t$
$(iii)$ $e^{-\omega t}$
$(iv)$ $\log(\omega t)$

Define the amplitude of $SHM$ and draw two different $SHM$s in one figure having two different amplitudes.

Identify the function which represents a non-periodic motion.

$A$ particle is executing simple harmonic motion with time period $2 \ s$ and amplitude $1 \ cm$. If $D$ and $d$ are the total distance and displacement covered by the particle in $12.5 \ s$,then $\frac{D}{d}$ is:

$A$ particle executes simple harmonic motion with an amplitude '$A$'. The distance travelled by it in one periodic time is