Question

Analyze the response of the system, using matlab X"-4x'-5x = cosh (at); *(0) = 1, *'(0)=4

Answer 1

In matlab I have done it using lsim as well as ode45.

lsim code:

A = [0 1;5 4];
B = [0;1];
C = [1 0;0 1];
D = 0;
sys = ss(A,B,C,D)
t = 0:0.01:1;
ic = [1;4];
u = cosh(2*t);
figure(1)
lsim(sys,u,t,ic)

out(1) shows displacement responce and out(2) shows velocity responce.

Linear Simulation Results 150 100 To: Out(1) 50 Amplitude 0 800 600 To: Out(2) 400 200 0 0 0.1 0.2 0.3 0.7 0.8 0.9 1 0.4 0.5 0.6 Time (seconds)

by ode 45:

function:

function dydx = odefun(t,y)
    dydx = [y(2);5*y(1)+4*y(2)+cosh(2*t)];
end

code:

[t,y] = ode45(@(t,y) odefun(t,y),t,ic)
figure(2)
plot(t,y(:,1),'displacement response')
figure(3)
plot(t,y(:,2),'velocity response')

after saving the function, run the code in matlab.

upvote my answer.