$1.(\backslash (\backslash$mathbf$\{25\}\backslash )$ points$)$ Draw sample input and output graphs versus time and give sample equations for the following systems. For each system, choose an input signal and plot a typical corresponding output graph for the given system type. Use multiple input signals if necessary to demonstrate the system property. Also give sample equations for each system.

a$)$ Static, time varying, and nonlinear

b$)$ Static, time invariant, and linear

c$)$ Dynamic, time varying, and nonlinear

d$)$ Dynamic, time invariant, and nonlinear