- #1
viciado123
- 54
- 0
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] ?