- #1
LagrangeEuler
- 717
- 20
In case of equation
[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.
[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.