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 [itex]z^2+ a= 0[/itex] and now you know that the solutions are [itex]z= -5.71839 i[/itex] and [itex]z= 5.71839 i[/itex].

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

So your solutions are [itex]cos(5.71839 t)[/itex] and [itex]sin(5.71839 t)[/itex]

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