Question: How Do I Use Results from dsolve/numeric to Create Post-Processing Functions



I'm new to Maple; well, I've been 'away' from Maple for a number of years and now I have several compelling reasons to get back into the thick of parts of Maple.

I constructed a very simple ODE model of dropping a mass from a height h and letting it hit a massless platter on a spring, with the other end of the spring connected ground.  One can use energy methods to derive the "apprent" weight experienced by ground.  The point is I know what the solution should be, the problem is simple, and therefore setting it up and solving it with Maple serves as way to instruct myself.  However, the answers to my following questions could not be found, by me, in the help system that ships with Maple (14).

The differential equation is ordinary second order, but non-linear since the force of the spring on the mass is discontinuous (piecewise).  What I presented to Maple in the way of solution options was probably overkill, but I have in mind submitting to Maple much, much larger and more complicated systems in the future, and I intend on using practically the same options.  I used the range option and a halting event, the event being the mass velocity zero so that I get the maximum 'apparent' weight to ground and then stop the simulation.  Also, using range and halt event means when I want to post-process, Maple does not have to re-calculate.  My questions regard post-processing.

I believe the results are effectively interpolating functions, in the form of Maple procedures.  The output seems to include time, and the zeroth and first derivative of the displacement.  However, I want to determine, and subsequently use, the second derivative (acceleration).  Also, I want to define a fucntion of time, based on the returned solution that gives me the force in the spring (the apparent weight experienced by the ground as a function of time) so I can plot it and use it in further post-processing tasks.

I have included in the worksheet four questions, three of which I just wrote above (please forgive me if it is in 'bad' form; as I wrote above, I've been away from Maple for a long time).

Many thanks in advance for any responses. 


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