# Small amplitudes and Stokes drag law

Why is it that on a damped harmonic oscillator or a pendulum in a fluid, the Stokes drag law in the fluid only applied to small amplitude oscillation compared to large amplitudes oscillations?

Dose for a large amplitudes have different effect on the velocity compared to small amplituded?

note: I have recently come across some new information, about to why this is the case the issue is the paper I have found only give a brief outline on the reasoning, and I would like to have more literature to read. I have googled the method with little success and was wondering if anyone could maybe expand a bit more on what has been outlined in the paper.

http://ftp.aip.org/epaps/phys_teach/E-PHTEAH-55-015709/555_appendix.pdf

If you have a masse which oscillate $$x(t)=a\sin (\omega t)$$ , the speed is $$v(t)=\omega a\cos (\omega t)$$and so the maximum is $${{v}_{\max }}=\omega a$$
To apply Stokes law, a necessary condition is that the Reynolds number must be small compared to $$1$$ : $$\operatorname{Re}=\frac{\mu {{v}_{\max }}d}{\eta }=\frac{\mu \omega ad}{\eta }\ll 1$$ and so $$a\ll \frac{\eta }{\mu \omega d}$$