91Ó°ÊÓ

Distance from the origin the given function is$s=5\sin (t-\mathrm{Ï€})$

Time Period (T) : It is the time taken by the motion to repeat itself. So the unit of a time period is seconds.

Frequency (f) : It is defined as a number of times the motion is repeated in one second. The unit of frequency is Hz (Hertz).

Frequency is related to Time period as f = 1/T.

Following is the distance function:

$s=5\sin (t-\mathrm{Ï€})$

Amplitude is the maximum value of distance from the mean position.

So, amplitude = 5 .

The distance functions of the form$A\sin (\mathrm{Ó\neg }t-\mathrm{Ï•})$.

So, $\mathrm{Ó\neg }=1$.

Then, obtain values:

Period $=\frac{2\mathrm{Ï€}}{\mathrm{Ó\neg }}$

Period $=\frac{2\mathrm{Ï€}}{1}$

Period $=2\mathrm{Ï€}$

The frequency is defined as the inverse of the period.

So, .$\text{Frequency}=\frac{1}{\text{period}}$

Frequency $\frac{1}{2\mathrm{Ï€}}$

$\begin{array}{rcl}s& =& 5\sin (t-\mathrm{Ï€})\\ \frac{ds}{dt}& =& 5\cos (t-\mathrm{Ï€})\end{array}$

So, velocity amplitude is 5.