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.