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## Main Question or Discussion Point

Damped vibration

[tex] m \frac{d^2x}{dt^2} + \gamma \frac{dx}{dt} + kx = 0 [/tex]

Characteristic equation is

[tex]mr^2 + \gamma r + k = 0[/tex]

[tex]r_1 = \frac{- \gamma + \sqrt{( \gamma )^2 - 4mk}}{2m}[/tex]

[tex]r_2 = \frac{- \gamma - \sqrt{( \gamma )^2 - 4mk}}{2m}[/tex]

In overdamped

[tex]( \gamma )^2 - 4mk > 0[/tex]

What I need to calculate to find the general solution:

[tex] x(t) = C_1 e^{r_1 t} + C_2 e^{r_2 t}[/tex] ???

[tex] m \frac{d^2x}{dt^2} + \gamma \frac{dx}{dt} + kx = 0 [/tex]

Characteristic equation is

[tex]mr^2 + \gamma r + k = 0[/tex]

[tex]r_1 = \frac{- \gamma + \sqrt{( \gamma )^2 - 4mk}}{2m}[/tex]

[tex]r_2 = \frac{- \gamma - \sqrt{( \gamma )^2 - 4mk}}{2m}[/tex]

In overdamped

[tex]( \gamma )^2 - 4mk > 0[/tex]

What I need to calculate to find the general solution:

[tex] x(t) = C_1 e^{r_1 t} + C_2 e^{r_2 t}[/tex] ???