# Damped driven harmonic oscillator in a steady state

In the limit as t goes to infinity the solution approaches

x(t)=Ksin[ω(t-t0)]

where K and t0 depend on ω (note: t0 = t subscript 0)

I am attempting to show that K(ω) = 1/(ω^4-ω^2+1)^1/2 and failing

My thoughts:

I believe that at t=0. The only important part of the general solution to the original equation is the exponential part (because e^0=1while as t increases (and eventually to the limit) only the particular solution is of importance

hence i have tried equating Ksin[ω(t-t0)] with the particular solution and failing.

https://brainmass.com/math/basic-algebra/damped-driven-harmonic-oscillator-steady-state-563122

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The solution shows how to solve the damped driven harmonic oscillator equation and how to writethe solution as a single sine wave with a constant phase.