3. (35pts; including 10 bonus pts) For the system shown below:
f
k2
b1
k1
WE
m
G(s) = \frac{X(s)}{F(s)}
b2
X
(1) (10pts) Find the transfer function G(s) as a function of m, b1, b2, k1, k2. What is the order of this system?
(2) (15pts) The system parameters are given as shown below. As the b? value is small, you could model this
system without considering the b? value (i.e., set b? = 0). What is the order of the system now? Then,
find the settling time ($T_s$) and percent overshoot (%OS) of a step response of this system.
m = 1 kg, b? = 0.2 Ns/m, b2 = 1 Ns/m, k? = 1 N/m, k2 = 2 N\cdot s/m
(3) (10pts: bonus) Use MATLAB to plot step responses of the two systems (one with the original system, and
the other with the approximated system by setting m = 0) in the same figure and check whether the system
approximation is valid.