(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

This is a portion of a slightly larger problem involving:

[tex]

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

[/tex]

[tex]

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

[/tex]

I would like to check my work and I don't believe I am moving toward the solution, knowing it has sin and cos in the final solution:

2. Relevant equations

3. The attempt at a solution

I'm just wanting some help on the math portion of the following -

Picking up midstream in a problem - I have started with a substitution

[tex]

u= \frac {dx}{dt}

[/tex]

[tex]

K1 \frac {du^{2}}{dt^2} + {-K2}u = 0

[/tex]

[tex]

u = e^{mt}

u’ = me^{mt}

u’’ = m^2e^{mt}

[/tex]

[tex]

K2*m^{2}e^{mt} + -K1* e^{mt} = 0

[/tex]

Factor out [tex] e^{mt} [/tex]

[tex]

m^2 = \frac {K1}{K2}

[/tex]

[tex]

m =sqrt{ \frac {K1}{K2}}

[/tex]

I am 1 integration away from getting X.

I know the solution is of the form X = Acos(at) + Bsin(at) - I was expecting complex roots.

If the above is correct then my problem is further upstream

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Solving a 2nd order differential equation

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