solving Tuned Mass Damper using ODE45, need help putting in equation as parameter to solve

For a tuned mass damper the equations are as follows:

=

=

In matrix form using the companion matrices and

:

= * +

F =

initial condition given vector is

and the interval is

Given the values of the variables the Matrix becomes

=* +

I am told to make a matlab script to solve this numerically and so far i have:

m1 = 1;

m2 = 0.05;

k1 = 1;

k2 = 0;

b1 = 0.001;

b2 = 0;

om = 0.95;

%Numerically solve DE

x0 = [0;0;0;0];

tvec = linspace(0,7000,35000);

A = [ 0, 0, 1, 0;

0, 0, 0, 1;

-(k1+k2)/m1, k2/m1, -(b1+b2)/m1, b2/m1;

k2/m2,-k2/m2, b2/m2,-b2/m2;]

%Hint given to use to solve this:

[t,x] = ode45(@(t,x) ___ + [_;_;_;_],tvec,x0);

I see that in the hint an equation has to go in the red underline plus a column vector. I'm assuming that this column vector that goes affter the plus is .

After i put in the values of the variables in Matrix A and multiplied it by the column vector of [x1; x2; y1; y2;] i get:

and given the subsition i used of does this become

Answer 1

[Jan]

As far as I can see, you have everything you need already.

[t,x] = ode45(@(t,x) A * x + [0; 0; sin(om*t); 0], tvec, x0);

If you write: "No matter what i try i either get an error that the arrays in the equation do not match", post your code an a copy of the error message. Then we can help you.

[Proximus]

My apologies, the error was:

Error using +

Matrix dimensions must agree.

And the reason why was because i was manually putting in the equation in there as the column vector of the result of A*x as:

[t,x] = ode45(@(t,x) [x1; x2; -x -b1*x(1);0] + [0; 0; sin(om*t); 0], tvec, x0);

When it didn't dawn upon to just put A*x there instead. Thanks.