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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 vt Rit Impedance V I R Electronic components: Capacitors: • Voltage is proportional to integral of current Voltage Current Impedance V I i t v t 1 vt 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-