Very nice, I have seen similar problems. I posted here once that I could not solve a trivial problem where the drag varied as the cube of the velocity.
The only way I could solve it was using a Taylor expansion. I plotted but the solution curved seemed a little odd. I could not find a...
What are the assumptions for the drag of this problem? -kv^3 ?? squared?? Also, I have read that this has something to do with an object bouncing of a wall. Hmmm can anyone post the original problem in differential equation form?
Maybe I can solve it today and create another...
Oh, I think I might have found a better method that involves a polynomial solution. Maybe just by iteration using the Taylor series. The problem does not say anything about I.C s but I cannot think of anything else. xD
Thank you
Your solution is very elegant. Although the book calls for a power series solution ( at least first 4 terms). I was reviewing from my ODE books but like always math books turn out not to have the thing you are looking for. hehe
Nevertheless thanks for taking the time to solve it...
Well,
I have attempted to guessv = \Sigmac_{n} t ^{n}
But my problem is the cubed term. Series solutions seem to only be easy when dealing with polynomial coefficients, but this time the dependent variable is causing the non-linearity of the ODE.
I have ofcourse substituted the derivative...
Homework Statement
I have not had luck in finding a solution that describes an object falling. Forces include gravitational force which is constant and a vicous force directly proportional to the cube of the velocity. I am supposed to find v as a function of time.Homework Equations
v' +...