$A$ particle is performing $SHM$ according to the equation $x = (3\, cm) \sin \left( \frac{2\pi t}{18} + \frac{\pi}{6} \right)$ where $t$ is in seconds. The distance travelled by the particle in $36\, s$ is ..... $cm$.

On an average,a human heart is found to beat $75$ times in a minute. Calculate its frequency and period.

Draw a graph of displacement of $SHM$ as a function of time.

$SHM$ is associated with what kind of motion?

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].
$(i)$ $\sin \omega t + \cos \omega t$
$(ii)$ $\sin \omega t + \cos 2\omega t + \sin 4\omega t$
$(iii)$ $e^{-\omega t}$
$(iv)$ $\log(\omega t)$

The function $\sin^2(\omega t)$ represents: