Name: __________________________________
Section: ______________________
ES 205
Examination I
April 1, 2009
Problem
Score
1
/35
2
/45
3
/20
Total
/100
Show all work for credit
AND
Turn in your signed help sheet
Name: __________________________________
ES 205 Examination I
1 April 2009
Problem 1
35 pts.
The circuit shown is called a “high-Q active bandreject filter”. Determine the equations
necessary to find the differential equation relating the input vi and the output vout (measured
with respect to ground). Be sure to clearly label all your variables on the circuit diagram. DO
NOT SOLVE THE EQUATIONS but clearly number you equations and list your unknowns.
Assume all the resistances and capacitances are known. Note: a indicates a soldered
connection.
C1
C2
a
-
vout
+
R1
b
R3
vi
R2
R4
C3
+
c
R5
Unknowns
Name: __________________________________
1 April 2009
Name: __________________________________
ES 205 Examination I
1 April 2009
Problem 2
45 pts.
The electro-mechanical system shown below is used to investigate the effectiveness of a new
spring-damper shock absorber. The permanent magnet DC motor provides the rocking motion
that is transmitted to the rear wheel via a rack and pinion gear set as shown, and the other
wheel is securely anchored to the ground. Set up the system of equations needed to relate the
, to the outputs, , , and . Clearly define all the unknown variables by labeling
input,
them in the picture (some have already been provided to you). Assume the output shaft of the
motor is rigid and that all system parameters are known. Do not find the EOM but number
the equations that you would use and generate a list of the unknown variables.
Mass = M
Mass moment of inertia=JG
Unknowns

L2
L1
G
x
SEP
SEP
k2
k1
Gear A and the
connected shaft have a
combined mass moment
of inertia of JA
y
JA
SEP
rA
mR
The rack is constrained to
move vertically.
k3
Vin
c2
Name: __________________________________
1 April 2009
Name: __________________________________
ES 205 Examination I
Problem 3
1 April 2009
20 pts.
You must show all work for full credit on these problems.
3.1 (4 pts) Draw the equivalent ideal model for the given system.
Beam: E, I, mbeam
m1
k
m2
3.2 (4 pts) Relate the input force Fin to the load force Fload in the arrangement of massless
gears below. The gears have n1 and n2 number of teeth, respectively.

n

Fin
n
Fload
Name: __________________________________
1 April 2009
3.3 (4 pts) Dr. Cunningham spilled his coffee on this step response plot and he cannot find
the data file used to make it. Using only the available information determine the damping
ratio. We do know that the initial conditions were 0
0
0.
2
Output (cm)
1.5
1
0.5
0
0
5
10
15
Time (sec)
20
25
30
Name: __________________________________
1 April 2009
3.4 (4 pts.) A block diagram for a system is shown below. Determine the natural frequency.
-
-
y
1
s
1
8
2
1
s
3.5 (4 pts.) Put the following equation in state space form using the state definitions,
, and
. The output is . Fill in the matrices below.
4∙
32 ∙
8∙
3∙
5∙
∙
∙
∙
∙
,