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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Harmonic oscillator with slight non-linearity

**Physics Forums | Science Articles, Homework Help, Discussion**