For the equation of motion (m ddot{x}+c dot{x}+k x=F(t)), with (m=9 mathrm{~kg}, c=4 mathrm{~N}-mathrm{s} / mathrm{m}, k=4

Question:

For the equation of motion $m \ddot{x}+c \dot{x}+k x=F(t)$, with $m=9 \mathrm{~kg}, c=4 \mathrm{~N}-\mathrm{s} / \mathrm{m}, k=4 \mathrm{~N} / \mathrm{m}$, and $F(t)$ is the unit step load, find the response. If the response is oscillatory, determine the possible modifications that need to be implemented to make the system critically damped. Plot both original and modified step response.