I need to find the initial conditions such than an underdamped harmonic oscillator will immediately begin steady-state motion under the time dependent force F = m f cosωt.(adsbygoogle = window.adsbygoogle || []).push({});

For the underdamped case:

[tex]x(t) = ae^{-\gamma t}cos(\Omega t+\alpha)+\frac{f}{r}cos(\omega t-\theta)[/tex]

and if it matter, [tex]r^2 = (\omega^2_0-\omega^2)^2+4\gamma^2\omega^2[/tex]

and [tex]\theta = Tan^{-1}\frac{2\gamma\omega}{\omega^2_0-\omega^2}

[/tex]

I thought I would just have to find x0 and v0 such that the transient was 0, but that doesn't seem to be leading down the right track. What direction should my solution be heading?

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# Homework Help: How to begin oscillation in steady state?

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