Some other experiments:

When external forces are exerted on the system, the total energy is no longer constant, but influced under the action of the applied forces. It increases if the external foce helps "the system move faster" (doing positive work) and increases if it impedes the motion of the system (doing negative work).

Other topologies:

The network connection is specified by the symmetric matrix \(K\) which encodes the interconnection particles. The positive entry \(k_{ij}\) in \(K\) signifies a connection between particles \(i\) and \(j\) with spring with stiffness \(k_{ij}\). Since the Lagrangian coordinates for the system are the Cartesian \((x,y)\) positions of masses, the connection matrix \(K\) is converted to \(K_{global} = DWD^T\) before used in the equaitons. \(K\) is in fact the adjacancy matrix for the network graph. \(D\) is the incincidence matrix of the graph and W are the weights (stiffness) of the springs.