I have an interesting problem I have come across in my research. It results in the differential equation as follows:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]x''+2γ(x')^\nu+\omega_{o}^2x=g(t)[/itex]

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

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

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

Thanks!

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# Harmonic oscillator with slight non-linearity

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