6. For the electrical system shown below:
R
V
L
C
??
a. Prove that the transfer function between the output voltage, $v_o$, and input voltage, $v_s$,
is:
$\frac{V_o(s)}{V_s(s)} = \frac{Ls + R}{RCLs^2 + Ls + R}$
b. What is the order of the resulting transfer function?
c. If R = 1?, L = 1H, C = 1F, hand sketch the type of response will the system have to a
unit step input? (NOTE: You may ignore any numerator dynamics. Also, it is only a
sketch—the general shape must be apparent, but specific values do not need to be on
the sketch. Also, you may put it into Matlab to check your answer, but the Matlab
code and plot do NOT need to be submitted.)
d. How will your answer in part (c) change if it were a step input of magnitude 10?