Second-Order Matrix Differential Equation

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Shabeel Samad 2021-3-5

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编辑： Shabeel Samad 2021-3-8

I am attempting to solve a second-order differential for a double spring-mass-damper system. I was able to work out the math and obtain the differential equation in the format Mx" = Kx' + Bx + F.

M,K,B and F are matrices.

M= [m1 0 0; 0 m2 0; 0 0 m3];

K= [-k1 k1 0; k1 -k1-k2 k2; 0 k2 -k2];

B= [-b1 b1 0; b1 -b1-b2 b2; 0 b2 -b2];

F= [f 0 0];

All variables inside the matrices are random integers. I attempted to approach this in Simulink and also as a system of first order differential but my knowledge in MATLAB was not sufficient to use it as a matrix.

Any help is much appreciated!

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James Tursa 2021-3-8

What do you mean by "All variables inside the matrices are random integers"? That you are starting the system off with random parameters but these parameters remain fixed throughout the simulation? Or that you have some type of stochastic system where the parameters change randomly during the simulation?

Shabeel Samad 2021-3-8

编辑：Shabeel Samad 2021-3-8

Random in the sense that the variable you use can be anything you want. I didnt want to assign numbers when I posted the question. I felt that this would make it easier to solve.

m1 = 1

m2 = 1

m3 = 2

k1= 5

k2 = 10

b1= 2

b2 = 3

f1 = 10sin(30)

Providing integars seems easier to understand. I apologize for complicating the system for no reason.

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