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## Main Question or Discussion Point

How to get overdamping condition of equation

[tex]m\ddot{x}+\dot{x}+kx=0,[/tex]

Taking ##x=\mbox{e}^{\lambda t}##, we got

[tex]\lambda_{1/2}=\frac{-1 \pm \sqrt{1-4mk}}{2m}.[/tex]

Is it possible from this ##\lambda## values to got overdamped condition?

I found that if we have equation

[tex]m \ddot{x}+\gamma \dot{x}=f(x),[/tex]

then ##-4m\frac{\partial f}{\partial x} \leq \gamma^2## is overdamped condition. How to find it? Any help?

[tex]m\ddot{x}+\dot{x}+kx=0,[/tex]

Taking ##x=\mbox{e}^{\lambda t}##, we got

[tex]\lambda_{1/2}=\frac{-1 \pm \sqrt{1-4mk}}{2m}.[/tex]

Is it possible from this ##\lambda## values to got overdamped condition?

I found that if we have equation

[tex]m \ddot{x}+\gamma \dot{x}=f(x),[/tex]

then ##-4m\frac{\partial f}{\partial x} \leq \gamma^2## is overdamped condition. How to find it? Any help?