Question

Solve the differential equation \frac{d^2x}{dt^2} + \kappa \frac{dx}{dt} = -\omega^2 x where \kappa and \omega are real numbers, by using the following solution as an ansatz x(t) = Ae^{i\phi}e^{Wt} Plug this solution into the differential equation and find an expression for \textit{W} in terms of \kappa and \omega. You could use the quadratic formula to solve the quadratic equation you will find. Remember that quadratic equations always have two solutions. Notice that \textit{W} could be either real or complex, depending on the values of \kappa and \omega.

          Solve the differential equation
\frac{d^2x}{dt^2} + \kappa \frac{dx}{dt} = -\omega^2 x
where \kappa and \omega are real numbers, by using the following
solution as an ansatz
x(t) = Ae^{i\phi}e^{Wt}
Plug this solution into the differential
equation and find an expression for \textit{W} in terms of \kappa and \omega.
*You could use the quadratic formula to solve the
quadratic equation you will find. Remember that
quadratic equations always have two solutions.*
Notice that \textit{W} could be either real or complex,
depending on the values of \kappa and \omega.

Solve the differential equation
(d^2x)/(dt^2) + κ(dx)/(dt) = -ω^2 x
where κand ωare real numbers, by using the following
solution as an ansatz
x(t) = Ae^iϕe^Wt
Plug this solution into the differential
equation and find an expression for W in terms of κand ω.
*You could use the quadratic formula to solve the
quadratic equation you will find. Remember that
quadratic equations always have two solutions.*
Notice that W could be either real or complex,
depending on the values of κand ω.

Added by Virginia P.

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