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## Homework Statement

Greetings –

I am wanting to solve the following system of differential equations:

[tex]

K*\frac{d^2x}{dt^2} = -K2*\frac{dz}{dt}

[/tex]

[tex]

K*\frac{dz^2}{dt^2} = K2*\frac{dx}{dt}

[/tex]

## Homework Equations

## The Attempt at a Solution

Now – I am not just wanting to solve it (I know what the solution is already) I am wanting for grins to solve it as if I was back in school –

I would like to solve this system 2 ways:

Am I correct that using Laplace transforms are a straightforward way to solve this system?

I have scanned my old diff. e. book and could not find great examples of solving systems.

Can I use the method where I would set:

x = i1

x’ = i2

x” = i3

then i1’ = i2

i2’ = i3

Likewise for z

z = j1

z’ = j2

z’’ = j3

j1’ = j2

j2’ = j3

ending up with:

K(i2’) = -(k2)j2

K(j2’) = (k2)i2

What I don’t know how to do is solve this system using a typical tool - something like pulling out the characteristic equation or so forth?

Can you help – how can I solve this system (a second method other than Laplace)?

Thanks

-Sparky_