.ScalableTestSuite.Mechanical.HarmonicOscillator.Models.HarmonicOscillator

Information

This model represents an N-dimensional mechanical translational system. The masses are not directly connected by springs; rather, a linear network of massless springs connects N massless nodes, which are in turn connected to the masses via other massless springs. As a consequence, a large system of sparse linear equations needs to be solved to compute the accelerations of the masses.

The most interesting feature of this simple system is that the DAE formulation is sparse, since each system equations refer to at most three nodes at a time, while the ODE formulation is dense, because the acceleration of each point mass depends on the posistion of all other masses.

This type of coupling is also found in other more complex models, such as multi-body systems with many rigid links (see models in the FlexibleBeam and Strings packages) and electro-mechanical models of power generation and transmission systems. The present model can be used to demonstrate the effect of this structural property with the minimum amount of overhead.

The transient is initiated by perturbing the initial condition of the first point mass with respect to the rest equilibrium condition.