- #1

LagrangeEuler

- 704

- 19

[tex]\alpha y''(x)+\beta y'(x)+\gamma y(x)=0 [/tex]

where ##\alpha>0##, ##\beta>0##, ##\gamma>0##, characteristic equation is

[tex]\alpha r^2+\beta r+\gamma=0[/tex]

and characteristic roots are

[tex]r_{1,2}=\frac{-\beta \pm \sqrt{\beta^2-4\alpha \gamma}}{2 \alpha}[/tex]

If ## \beta^2<4\alpha \gamma## system is underdamped, and

if ## \beta^2>4\alpha \gamma## system is overdamped.

What in the case of equation

[tex]\alpha y''(x)+\beta y'(x)+\gamma \sin[y(x)]=0 [/tex]

when equation is nonlinear? How to find when system is overdamped? Thanks a lot for your help in advance.