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3 Computer Simulation of Dynamic Systems
Fig. 3.29 Graphs of the displacements of individual springs and a graph of their resulting
displacement in series connection
is rigidity of an equivalent spring capable of replacing two real springs connected
“in series.” The differential equation of motion of the body also does not contain any
complicating elements:
m
d
2 x
dt 2 = −
k 1 + k 2
k 1 k 2
x
Similarly, to the previous experiment, we take two springs with stiffness k 1 = 0.4
kg/s
2 (yellow line) and k 2 = 0.6 kg/s
2 (green line) and connect them in series. Get a
blue graph. It coincides with the spring displacement schedule with stiffness k = 4.17
kg/s
2 , which is consistent with the theoretical formula, as shown in Fig. 3.29.
3.4 Universality of a Computer Model and Equivalent
Physical Systems
Any dynamic system corresponds to some physical model. It may turn out that
the same physical (or mathematical) model is used to describe systems that are
completely different in nature. Let us consider this case as an example of oscillatory
systems [8].