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(spring.mdl)

 

Consider the problem of a spring pushing a weight on a frictionless horizontal surface.  

You need to be sure to use Runge-Kutta integration when simulating this model to get the correct result.  This is the simplest structure that can generate oscillations, and the oscillations are undamped.

Consider the closely related problem of a constancy that uses time not spent doing billing work to bring in new clients (consult.mdl):

This model is driven by a step increase in total hours.  It also has a somewhat involved set of initialization equations and is shown with these links hidden.

The striking thing in comparing these two oscillating models is the addition of the two extra loops in the second model.  It is actually quite rare to get a single loop with more than a single level in business systems.  The rule is that there are likely to be a number of minor negative loops and these, in general, will be damping.

It is a useful exercise to experiment with changing constants in these to models and understanding how they influence behavior.  The Workforce Inventory model in Chapter 2 and the discussion in Chapter 8 go further into oscillation.