HELP Characteristic Equation question

[Gspace]

Homework Statement

Come up with the frequency directly from the solutions of the characteristic equation.

{{z=0.-5.71839 i},{z=0.+5.71839 i}}

Homework Equations

characteristic equation = z^2+b z+c=0

The Attempt at a Solution

Not sure where to start. Any help would be greatly appreciated.

 

[HallsofIvy]

You have left out a heckuvalot! Please don't ask other people to guess what you are doing.

My guess, however, is that you have a differential equation of the form x"+ ax= 0 which has characteristic equation $z^2+ a= 0$ and now you know that the solutions are $z= -5.71839 i$ and $z= 5.71839 i$.

You should know that is $\alpha i$ and $-\alpha i$ are solutions to the characteristic equation of a linear, homogeneous, differential equation with constant coefficients, then the solutions are linear combinations of $cos(\alpha t)$ and $sin(\alpha t)$.

So your solutions are $cos(5.71839 t)$ and $sin(5.71839 t)$

Those will complete one cycle when $5.71839 t= 2\pi= 6.28318$. That will tell you the period and the frequency is the reciprocal of the period.