Calculate Piecewise Function and its Visualization

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Write a MATLAB program to evaluate and plot the piecewise function $f(t)$ described below versus $t.$ The plot should be appropriately annotated.

$f(t)=\{\begin{array}{cc}{A}_{1}cos({}_{1}t+{}_1),& 0t<mn\; id="EditorElement\_568370">0</mn><mn\; id="EditorElement\_568371">.</mn><mn\; id="EditorElement\_568372">5</mn><mi\; id="EditorElement\_568374">s</mi>\\ A_{1}cos({}_{1}t+{}_1)e^{-bt},& 0\mathrm{.}5t1\mathrm{.}5s\end{array}$

Execute your program for two cases:

$A1=8\mathrm{.}5,{}_1=20ra\frac{d}{s},{}_1=-\frac{}{2}$rad,$b=1\mathrm{.}75$

and

$A1=8\mathrm{.}5,{}_1=20ra\frac{d}{s},{}_1=-\frac{}{2}$rad,$b=2\mathrm{.}75$

Hints: you can create separate arrays for the two time ranges $t1$ and $t2,$ evaluate the piece$-$wise function $f(t)$ for each piece $t1$ and $t2($creating $f1$ and $f2),$ and then concatenating the $t$ pieces and the $f(t)$ pieces for plotting $f(t)$ versus $t.$

In MATLAB the function exp$(x)$ gives the value of the exponential function $e^x.$

Use something like $)<mi\; id="EditorElement\_567438">(</mi><mn\; id="EditorElement\_567428">0</mn><mn\; id="EditorElement\_567429">.</mn><mn\; id="EditorElement\_567430">5</mn>$ as the end boundary of the first range.