Obtain the following requirements for a simple mass-spring-damper system with input of force f, output of displacement x, and translational motion only along the horizontal axis. a) Equation of...

Obtain the following requirements for a simple mass-spring-damper system with input of force f, output of displacement x, and translational motion only along the horizontal axis.
a) Equation of motion,
b) state space model,
c) transfer function G(s),
d) the time domain expression of the output according to the unit step function input,
e) permanent regime error to be observed at the output according to the unit step function input,
f) pole and zero positions in the complex plane,
g) its absolute stability,
h) the undamped natural frequency,
i) damping ratio,
j) damped natural frequency,
k) open loop/static/dc gain,
l) maximum overshoot (Mp),
m) peak time (tp),
n) settling time (ts, 2% tolerance).