Question

Consider the following second-order ODE representing a spring-mass-damper system for zero initial conditions (forced response): where u is the Unit Step Function (of magnitude 1 a. Use MATLAB to obtain an analytical solution x() for the differential equation, using the Laplace Transforms approach (do not use DSOLVE). Obtain the analytical expression for ao. Also obtain a plot of x() (for a simulation of 14 seconds) b. Obtain the Transfer Function representation for the system. c. Use MATLAB to obtain the Step response graph of the system, using the Transfer Function found in part (b). Compare this graph with that obtained in part (a). d. Obtain a numerical solution for the above ODE, using Simulink. Run the Simulink model for 14 seconds and compare the x plot with that obtained in parts (a) and (c) Submit screenshots of the Simulink model, and the Scope output.

Answer 1

`Hey,

Note: Brother in case of any queries, just comment in box I would be very happy to assist all your queries

clear all
clc
syms x(t) Dx(t)
eq=2*diff(x,2)+2*diff(x)+x==heaviside(1);
Dx=diff(x);
cond=[x(0)==0 Dx(0)==0];
f=matlabFunction(dsolve(eq,cond));
fplot(f,[0,14]);

Note: Brother according to HOMEWORKLIB RULES we are only allowed to answer first part if there are many. So, I request you to post other part as separate posts.

Kindly revert for any queries

Thanks.