Non$-$Book $1$

a$)$ Write your own custom Newton$-$Euler single step code.

b$)$ Plot the output of each state represented in $5\mathrm{.}15$ from $0$ to $10$ seconds given initial conditions $z_1^{}=0,z_1=\mathrm{.}05,$ and $z_2=-\mathrm{.}03$ and with input $f_a(t)=0\mathrm{.}01,m=1,k=0\mathrm{.}2,b=0\mathrm{.}1.($Note$,$ there are no units in this system$).$

c$)$ Experiment with different $t$ values and compare your results.