Interpolating Functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg81760] Interpolating Functions*From*: "James Ransley" <james.ransley at gmail.com>*Date*: Wed, 3 Oct 2007 02:25:47 -0400 (EDT)

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