Signals and Systems

$2\mathrm{.}1$ Plot the continuous$-$time signal $x(t)=\frac{t}{1+t^4}.$

Find the equation for and plot the signals.

a$.x(1\mathrm{.}5t)$

b$.x(0\mathrm{.}8t)$

c$.x(-t)$

d$.x(t+3\mathrm{.}6)$

e$.x(-2t)$

f$.x(2t-1)$

g$.x(-0\mathrm{.}7t-0\mathrm{.}35)$

$2\mathrm{.}12$ Plot the following signals and their even and odd parts.

a$.x(t)=e^{-|t-1|}$

b$.y(t)=\{\begin{array}{cc}2,& -1t3\\ 0,& \text{e}\text{l}\text{s}\text{e}\text{w}\text{h}\text{e}\text{r}\text{e}\end{array}$

c$.z(t)=3sin(6t)$

d$.w(t)=4cos(2t-\frac{}{4})$

$2\mathrm{.}15$ Write the system equation for the electric circuit shown in Figure $2\mathrm{.}27.$ The voltages $x(t)$ and $y(t)$ are the input and output, respectively.