A system is represented by $m{x}^{}+kx=f$ where $m=1kg$ and $k=9N\frac{s}{m}.$ Use the initial

conditions: $x(0)=0m$ and $x^{}(0)=1\frac{m}{s}.$

a$)$ Solve the equation to obtain the response, $x(t),$ of the system when $f=9.$

b$)$ Solve for the characteristic roots.

c$)$ Also, what is the natural frequency, ${}_n,$ of the system?

d$)$ What is the damping ratio of the system?

e$)$ Is the system undamped, underdamped, critically damped, or over damped?