$1.(25$ points$)$ Draw sample input and output graphs versus time 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.

a$)$ Static system

b$)$ Dynamic system

c$)$ Time invariant system

d$)$ Time varying system

e$)$ Linear system

f$)$ Nonlinear system