Harmonic oscillator with slight non-linearity

[groinsmash]

I have an interesting problem I have come across in my research. It results in the differential equation as follows:

x''+2γ(x')^\nu+\omega_{o}^2x=g(t)

Primes indicate the derivative with respect to t. \gamma and \omega are constants. The non-linearity comes from the first derivative x' which is raised to the power of \nu. \nu is known to be 0.12 but can be between 0 and 1. The cases where \nu=0 or \nu=1 are easy enough. But how to go about tackling an arbitrary \nu?

The problem may be made easier by noting that g(t)=1 for t\geq0 and 0 for t<0.

Any ideas on how to go about solving it? Numerically or analytically (which would be amazing).

Thanks!

 

[jackmell]

You gotta' get Mathematica. Here's some Mathematica code:

\[Gamma] = 0.25
\[Nu] = 0.5; 
\[Omega] = 0.1
mysol = NDSolve[{Derivative[2][x][t] + 
      2*\[Gamma]*Derivative[1][x][t]^\[Nu] + \[Omega]*x[t] == 
     1, x[0] == 1, Derivative[1][x][0] == 1}, x, 
   {t, 0, 5}]
Plot[x[t] /. mysol, {t, 0, 5}]