Example test questions for PM
1. In the Researching phase of the engineering design cycle: state and describe at least five
(5) steps when defining the problem.
2. Given a system has the following instantaneous (dynamic) relationships, sketch their
characteristic graphs on appropriate axes:
i) y ∝ x
ii) y ∝ dx/dt iii) y ∝ d2x/dt2
Initially a system starts with a component with the relationship given in (i) sketch its time
response to a step change in the effort variable. Plot both the input and output on the
same axes (Hint: time is the independent variable).
An additional component with the relationship given in (ii) is added; add the new time
response clearly labelling the graph.
Finally, a component described by (iii) is added; plot and discuss the possible outputs.
3. Given two resistors are in parallel in a connected circuit with a unit voltage effort driving
the current flow, draw the diagram labelling important components, variables and
constants.
Calculate the equivalent resistor value for the circuit.
• Help session available in AM103, @5 PM, with Elf
Physical Modelling:
1.
2.
3.
4.
5.
6.
Out there world inside here
Modelling and Design Cycle
Practical example: Passive Dynamic Walkers
Base systems and concepts
Ideals, assumptions and real life
Similarities in systems and responses
Design Cycle:
https://stillwater.sharepoint.okstate.edu/ENGR1113/default.aspx
Similarities in systems and responses:
1. Similarities in systems
– why is a spring like a water tank like a capacitor???
2. First derivative time response
3. Second derivative time responses (note there is more than one!)
4. Damping
5. Parallel verses Serial connection of components
Electronic components: Resistors:
• Voltage is proportional to current, Ohms law V = RI
i t 
v t 
Voltage Current
vt   Rit 
Impedance
V I
R
Electronic components: Capacitors:
• Voltage is proportional to integral of current
Voltage Current
Impedance
V I
i t 
v t 
1
vt    i t 
C
1 1

C s
[think of s as the rate of change of output variable in an instant]
Electronic components: Inductors:
• Voltage is proportional to integral of current
Voltage Current
i t 
v t 
di t 
v t   L
dt
Impedance
 V s  I s 
Ls
Modelling: Dynamic Systems
www.millhouse.nl
www.pbase.com
Modelling: Dynamic Systems
Consider dynamic systems: these change with time
As an example consider water system with two tanks
Water will flow from first tank to second
[Assume I stays constant due to nature of Dams]
Plot time response of system….?
Dynamic Systems
Pressure
Pressure
Water flows because of pressure difference
[Ignore atmospheric pressure – approx. equal at both ends of pipe]
If have water at one end - what is its pressure? [Tanks with constant cross sectional area A]
Pressure is force per unit area, = F / A,
Force (F) is mass of water times gravity g
Mass of water (M) is volume of water * density
M=V*
Volume (V) is height of water, h, times its area A: V = h * A
Combining: pressure is
h *A*  *g
 h *  *g
A
I**g
L**g
For first tank, pressure is
For second tank, pressure is
Thus flow depends on (I-L) *  * g as well as on the pipe (its restrictance, R)
I-L
Flow 
*  *g
R
Flow changes volume of tanks:
Volume change = A * rate of change in height (L) = Flow
Thus rate of change in height
(dL/dt) = ?
A tank has a capacitance,
C =?
Thus rate of change in height L is
dL I - L
1

*  *g *
dt
R
A
C
A
 *g
?
Flow stops, and there is no change in height when I = L
dL I - L

dt R * C
Dynamic Flow
Level change – not instantaneous
• Initially: Large height difference  Large flow  L up a lot
• Then: Height difference less  Less flow  L increases, but by less
• Later: Height difference ‘lesser’  Less flow  L up, but by less, etc
Graphically we can thus argue
the variation of level L
and flow F is:
Time Response of System
Any system of the form:
O
K

I
1  T1s
[think of s as the rate of change of output variable in an instant]
Has a time response (depending on input):
Output
Exponential
Time
Time responses:
• Proportional components
Or
Ratio governed by constant of proportionality
x
f
Time responses:
• Proportional to derivative components (+ previous)
Or
Ratio governed by gain constant
Time of response governed by time constant
dx/dt
f
d2x/dt2
Time responses:
• Proportional to second derivative components (+ previous)
Or
Or
Ratio governed by gain constant
Time of response governed by time constants
Overshoot governed by damping constant.
f
Serial connection of components:
• Opposite to parallel connections
• What is equivalent spring?
Draw a free body diagram of a spring
Write down individual equations:
Consider laws to combine them:
Consider what does not change:
Ft = kxt
x t = x1 + x 2
Force must be equal on each spring
Can extend method to any number of springs in series
https://notendur.hi.is/eme1/skoli/edl_h05/
masteringphysics/13/springinseries.htm
Parallel connection of components:
• Opposite to serial connections
Remember to test:
• http://sploid.gizmodo.com/cool-newvideo-shows-nasas-flying-saucer-in-action-