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.

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