About solving state space equation (mass, spring, damper)

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Changwoo Lee 2022-10-1

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https://ww2.mathworks.cn/matlabcentral/answers/1815410-about-solving-state-space-equation-mass-spring-damper

回答： Sulaymon Eshkabilov 2022-10-1

采纳的回答： Sulaymon Eshkabilov

Hello, I have 4-DOF mass, spring, damper sysmtem.

1) My first question is how to construct the state space equation of the below diagram?

-The first force (F1) is imposed during the time t0~t1.

-Then, second force (F2) is imposed during the time t1~t2.

2) Then, within th time t0~t2, I want to get the each displacement (x1,x2,x3,x4)

In this case, how solve the system?

3) In my case, actually, F1 and F2 are not constants.

F1 is function of x3 (for example, F3=3*sin(x3))

F2 is function of x4 (for example, F4=2*cos(x4))

I'm eager for your answer. Thank you very much.

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William Rose 2022-10-1

@Changwoo Lee, this looks and sounds a lot like homework. This is not a homework site. Also, your quesitons are about math and physics, not Matlab. There are better sites for those questions - stack exchange for example.

Here are hints to get you started: for each mass, the equation is F = m*a = m*dv/dt = m*d2x/dt2. You can look at the diagram to determine the all the forces acting on each mass. Each mass has a position and a velocity. Those quantities are enough to describe the system.

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