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    Damped driven harmonic oscillator in a steady state

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    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.

    © BrainMass Inc. brainmass.com October 10, 2019, 6:58 am ad1c9bdddf
    https://brainmass.com/math/basic-algebra/damped-driven-harmonic-oscillator-steady-state-563122

    Solution Preview

    The solution is attached below in two files. The files are identical in content, only differ in format. The first is in MS Word format, while the other is in Adobe pdf format. Therefore, ...

    Solution Summary

    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.

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