# System of Second Order, Nonhomogeneous Differential Equations

1. May 7, 2008

### mccormas

Hello. I am an engineering student and am having trouble trying to figure out how to solve this system of second order, nonhomogeneous equations. I know how to solve a single second order, nonhomo. equation and how to solve a system of first orders, but not this one. Any help would be greatly appreciated. I have attached a scanned image of the equation because I couldn't format it right on here and it won't let me just post a URL because I'm new on here.

That is a g tucked in there on the right side of the equation. Thanks again.

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2. May 7, 2008

### trambolin

keeping in mind that you are an engineering student, I would speculate and assume that g is gravity, the masses are hanged from somewhere. and in general, you are required the solve the x(t) for each mass.

3. May 7, 2008

### mccormas

Exactly. I probably should have specified that earlier. The m's are masses, c's are damping coefficients and k's are spring constants. All are positive constants that will be specified by the user in the MATLAB program that I have to write. First, though, I need to figure out how to solve the problem by hand. Then I have to choose a numerical method we've learned and implement it in an M-file on MATLAB.

The problem has 3 masses hanging by springs and dashpots. We have to write the differential equations for the system and then solve it using a self-written m-file.

4. May 7, 2008

### trambolin

Then, define a new vector,

$$\hat x = \left( {\begin{array}{*{20}c} x \\ {\dot x} \\ \end{array}} \right)$$

From the fact
$$\frac{d}{dt}\hat x = \left( {\begin{array}{*{20}c} \dot{x} \\ {\ddot x} \\ \end{array}} \right)$$

Rewrite the equations again. and then solve a ODE set.