Thanks for the reply. So yes, I did realize this, but neither this or the 1/2 factor delivers an ODE that =0, they are just approximations (I decided to do both, and the plots show that ##\psi## has great boundary conditions as u approaches +- infinity, but needs some correction around the...
My god, something I can actually help with! (I'm an infrequent visitor here who just sponges you guys with my own questions!)
So hopefully in your "class" it was explained how at the turnover frequency that tau=1 (this can be seen better by plotting the log I vs log nu
Putting that (tau=1) into...
Fair enough, I'm being a bit lazy by asking really - I might try and go on with the non standard choice and see what happens, but as it's an approximation anyway I can't for the life of me see it affecting the 2nd half of the derivation, but I shall see, cheers!
At the point where we 'guess' a solution to this 2nd order ODE that cannot be done analytically, I was wondering why Griff and others choose $$e^{-x^2 / 2}$$ rather than just $$e^{-x^2}$$ I've plotted both here and am left wondering what's so different? If we guessed instead the unpopular...
Ah, thank you. I think I was having a mental block by insisting I have a definite integral from $$\int_{1}^{0} - \frac{1}{x} dx$$ in the first step which stopped any progress. That's excellent, thank you again, I really appreciate your help!
So using $$L=\frac{mv^2}{2} - \frac{1}{2} m lnx$$ and throwing it into the Euler-L equation I agree with kcrick & OlderDan that we can manipulate this to either $$\frac{d}{dt} m\dot{x} = -\frac{m}{2x}$$ or $$2vdv = -\frac{dx}{x}$$ but I'm not having any epiphanies on how to turn the above into...
Hi PF,
I am an old guy who found the value of education late in life - just finished a BSc (physics) at the ripe age 46 and I'm now thinking of teaching math.
Kind regards :)