Question

Objective: This activity has the purpose of helping students to to use either Simulink or VisSim to simulate the system behavior based on its Block Diagram representation and plot its response Student Instructions: The following spring-mass-damper system has no external forcing, that is Lu(0) 0. At time t"0 it has an initial condition for the spring, which it is distended by one unit; yO) 1. The system will respond to this initial condition (zero-input-response) until it reaches equilibriunm. | yin« 1 initial condibon for extenal orcing uin 0 no friction M=1.5 slugs B-4.0(Ibsecyft K-1 50bit Follow similar example 4.4 (Module 8) where instead of y, in this exercise we use x to denote displacement, and where instead of having an external forcing, in this exercise the extermal forcing is zero: u() 0 but with an initial displacement condition, y(o) 1, which is driving the system until it reaches equilibrium Help In Any" Can't reach this page an nouncement-rid-8027038-1/courses/SP-19-EE3002-80-SJU/SS-Sim-Proj-SP 1996281 %29pdf Required Project/Report Parts: Develop and use a free body diagram to write the system differential equation. 1. Sketch a Block Diagram realization of the system 2. 3. Model the previous Block Diagram system representation in VisSim or Simulink noting that it does not have an external forcing function (uin(t) 0) but it has an initial condition for the displacement (y(0) 1), which can be set at the appropriate integrator block 4. Plot the displacement y(t) and the velocity dy(O/dt of the system with time. Perform a Phase-Plane plot (velocity versus displacement). 5. verify that at 1.75 seconds the displacement is about x ~-0.0067754 6, 7. Verify that at 1.8 seconds the displacement is about x ~ 0.037855 Experiment with different values of M, K, B and initial condition. 8. Turn in: All parts as described above. MATLAB/Simulink or VisSim code/model for each part. Plots for each part correctly labeled. Include these instructions as the first page of your project wl 曲

Answer 1

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The SIMULINK block diagram is given below.

untitled File Edit View Simulation Format Tools Help Normal Integrator Integratori To Workspace Gain 150/1.5 Gain1 time Clock To Workspace1 Ready 100% ode45

set the initial conditions as given below for integrator 1.

Function Block Parameters: Integrator1 Integrator Continuous-time integration of the input signal. Parameters External reset: none Initial condition source: internal Initial condition: Limit output Upper saturation limit: inf Lower saturation limit: -inf Show saturation port Show state port OK Cancel Help Apply

Now simulate the model and execute the following code:

figure;plot(time,simout(:,1),time,simout(:,2),'linewidth',2);grid on;
xlabel('time');ylabel('Amplitude');title('states of the system');legend('velocity','position');

states of the system 6 -velocity position 4 a -2 -4 -10 0.5 2 2.5 3 1.5 time

code for phase plane plot:

figure;plot(simout(:,1),simout(:,2),'linewidth',2);grid on;
xlabel('velocity');ylabel('position');title('phase plane plot');

Phase plane plot is plotted below

phase plane plot 0.8 0.6 0.4 0.2 0.2 0.4 -0.6ト.. 0.8 -10-8 -6 -4 -2 4 6 velocity