In the case of the RLC circuit, the inductance L is 4 H and the capacitance C' is 1 F. In the
case of the
the mass is m is 4 kg and the spring constant k is 1 N/m.
mass-spring-damper,
1. Choose one model. Using Simulink, set-up the appropriate block diagram correspond-
ing to the governing differential equation (Equation 1 or 2). You'll also have to use a
scope to monitor both the forcing function (either Vert or Fert and the output (either V
or y. In the simulation, use a maximum step size of 0.01 (This is found in the "Model
Configuration Parameters" under the simulation tab. If the maximum step size is left
on auto, Simulink sometimes uses too large of a step and the outputs displayed in the
Scope box will be jagged rather than smooth). For the integrator blocks, the initial
condition is 0 at time 0. Run all simulations for 100 seconds.
The appropriate boundary conditions are either y(0) = 0 and y'(0) = 0 or V(0) = 0
and V'(0) = 0.
Finally, to introduce the forcing function into your block diagram use the "Step block"
found under sources. Choose a step time of 10 s, an initial value of 0, and a final value
of 10. If done correctly the forcing function will change from a value of 0 to 10 at 10
seconds./n2. Case 1: Run the simulation using either R = 0 or pf = 0N s/m.
3. Case 2: Run the simulation using either R = 0.62 or p = 0.6 N s/m.
4. Case 3: Run the simulation using either R= 1.52 or pf = 1.5N s/m.
5. Case 4: Run the simulation using either R = 32 or f = 3N s/m.
6. Case 5: Run the simulation using either R = 40 or y=4N s/m.
7. Case 6: Run the simulation using either R = 8N or pf = 8N-s/m.
8. Case 7: Run the simulation using either R = 16 or µ = 16 N. s/m.
9. Comment on your findings in Questions 2 through 8. In particular, you should find that
Case 5 separates Cases 2-4 from Cases 6 and 7 based on the roots of the characteristic
equation. Here, Cases 2-4 correspond to underdamped responses, Case 5 corresponds
to a critically damped response, and Cases 6-7 correspond to overdamped responses.
Case 1 corresponds to an undamped response. Here think about the influence of friction
(or resistance) on the response. Do the trends seem appropriate in terms of what we
understand about friction (or resistance)?/nDIRECTIONS:
Number your Answers!
Question 1: Show the block diagram that you used in Simulink with all blocks and signals
clearly labeled.
Questions 2-8: Show all 7 plots corresponding to each different value of either resistance
or coefficient of friction.
Question 9: Briefly discussion your findings in terms of the roots of the characteristic
equation. In particular, you should find that Case 5 separates Cases 2-4 from Cases 6 and
7. Here, Cases 2-4 correspond to underdamped responses, Case 5 corresponds to a
critically damped response, and Cases 6-7 correspond to overdamped responses. Case 1
corresponds to an undamped response. For each of these cases, calculate the damping
ratio. Comment on the effect of the dammping ratio on the type of transient response.
Save your assignment as a PDF and upload to the assignment submission window.
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