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Exam 1 Review:
MAE 3600 Winter 2021
• Login to Zoom on Friday at 7:50 am so I may proctor the
exam (leave your video on, mute the mic)
• Notes or textbook are not allowed
• You are allowed to use the 1-page equation sheet (see
Canvas)
• Time limit is 1 hr…. Scan and upload to Canvas by 9:15 am
Exam 1 Review:
MAE 3600 Winter 2021
• Exam 1 will focus on system modeling (Chapters 2-4)
• Exam will consist of 4 numerical problems like the Practice
HW problems and examples in class
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2
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Modeling Mechanical Systems
• Step 1: Draw FBD and use Newton’s 3rd law for equal-
and-opposite forces or torques
– Be mindful of the positive directions for displacements
– It may be useful to assume positive displacements or
velocities, or assume x2 > x1 (for example)
• Step 2: Sum forces (or torques) in positive direction
(Newton’s 2nd law, F = ma)
• Use the “sign rule” to check each 2nd-order ODE
Modeling Electrical Systems
• Step 1: Write the respective 1st-order ODE for each
energy-storage element (capacitor and/or inductor)
• Step 2: Use KVL (Loop law) and/or KCL (Node law) to
write all voltages or currents in terms of the acceptable
“dynamic variables” (eC and IL) and/or inputs (ein or Iin)
• Remember: voltage drop across a passive element (R, L,
C) is + to – (high voltage to lower voltage), i.e., eR < 0
• Move from – to + is a voltage rise, eR > 0
• Move from – to + across voltage source is a rise, ein > 0
3
4
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Modeling Electrical Systems (2)
• Ideal op amps:
– Draw negligible current, IA = 0
– Voltage difference at input terminals is zero,
– Gain K is infinite
• We can treat the connection thru the op amp as a “virtual
short” (connect to the ground)
0− AB ee
Modeling Electrical Systems (3)
• DC motors:
IKT mm =
Total electromagnetic
torque on the rotor
bb Ke = Back emf for DC motor
Electric circuit model is coupled with mechanical model
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6
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Modeling Hydraulic Systems
Fluid ODE:
Mechanical ODE:
System model
3rd-order nonlinear
system
( )xAQ
AxV
P  −
+
= in
0

( ) LFAPPkxxbxm −−=++ atm
Modeling Pneumatic Systems

−= V
RT
P
w
V
nRT
P  in inwPC =

Input mass-flow rate win could be choked or unchoked depending on P/PS
Supply tank has pressure PS
Assume compressible flow
through valve with orifice area A0
Basic ODE:
Rigid chamber (V = constant)
0
or





−



=
+

12
0
)1(
2
SS
Sd
P
P
P
P
RT
PACPC 

1
0
+
= rSd C
RT
PACPC 
rS CPP /
rS CPP /
if
if
(unchoked)
(choked)
Model
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Modeling Thermal Systems
• Apply the conservation of energy to each thermal boundary
Net rate of heat
energy stored
Time-rate of enthalpy
due to mass transfer
across boundary
Heat flow rates
across boundary
   −+−= outinoutoutinin qqTcmTcmTC pp 
T
R
q =
1
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