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Interpolating Functions

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.


Dr James Ransley
james.ransley at

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