Re: Interpolating Functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg81819] Re: Interpolating Functions*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>*Date*: Thu, 4 Oct 2007 04:23:10 -0400 (EDT)*Organization*: Uni Leipzig*References*: <fdvd39$sbc$1@smc.vnet.net>*Reply-to*: kuska at informatik.uni-leipzig.de

Hi, since you give no example I have to make my own sol = With[{gamma = 0.25, k = 1}, NDSolve[ {x''[t] + gamma*x'[t] + k*x[t] == 0, x[0] == 2, x'[0] == 0, \[ScriptCapitalL]'[t] == x'[t]^2/2 + k*x[t]^2/2, \[ScriptCapitalL][0] == 0}, {\[ScriptCapitalL][t], x[t]}, {t, 0, 20}][[1]] ] The energy loss is d\[ScriptCapitalE] = D[\[ScriptCapitalL][t] /. sol, t] and a plot of it is Plot[d\[ScriptCapitalE], {t, 0, 20}] Why you wish to integrate over time *after* you solve the equations of motion because NDSolve[] does nothing else than a time integration and in the worst case you get a waring that NDSolve[] will try to solve a differential algebraic equation. Regards Jens James Ransley wrote: > I am trying to calculate the total energy dissipated in the damper in > the damped harmonic oscillator problem with arbitraty forcing (in the > form of numerical data), for a range of spring constants and damping > factors (and for unit mass). Using Green's functions, I can get a > solution with analytic forcing functions, but I have problems when I > try to implement the same thing with a numberical forcing function. > > I can get as far as deriving (& plotting) the response of the system > in time for a given damping factor and spring constant, but I cannot > seem to differentiate this data - Mathematica complains that the > function being differentiated is not numeric. I think this is because > the function is a mix of time dependant interpolating functions and > anlaytic functions. It may be because I'm getting confused about the > definitions of differentiation for functions and > InterpolatingFunctions... What I want to do is differentiate the > response, square it and then integrate over time to get the energy > dissipated in the damper. It's kind of frustrating when you can plot > the response but you can't do this! > > It's rather a long notebook to post here - but if anyone thinks they > can help I'm happy to send the file. > > Thanks, > > Dr James Ransley > james.ransley at gmail.com >