5.8 Mechanical System with Two Springs and a Block
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SI.Length e2;
SI.Velocity v1;
SI.Velocity v2;
SI.Velocity v3;
SI.Force F1;
SI.Force F2;
SI.AngularVelocity w;
equation
// For spring 1:
F1 = k1*e1;
der(e1) = -v1;
// For spring 2:
F2 = k2*e2;
der(e2) = -v2;
// For block and load:
ML = if time < 5 then ML0 else 0;
(Mp + ML)*der(v3) = F1 + F2 - g*(Mp + ML);
v1 = v3 - Rp*w;
v2 = v3 + Rp*w;
J*der(w) = Rp*(F2 - F1);
// Initial equations
initial equation
der(e1) = 0;
der(e2) = 0;
der(v3) = 0;
der(w) = 0;
annotation(experiment(StartTime=0,StopTime=25));
//Specify the simulation time
end SpringPulleyLoad2;
The behavior of the hybrid model is reflected in the graphs Figs. 5.66, 5.67, and
5.68 where in the first 5 s the system is in lower stable equilibrium, after which an
event occurs—the load is removed from the unit and the system begins to oscillate.
When performing the third task, a problem arises related to the fact that the system
must be in equilibrium at certain spring extensions. This can be achieved by changing
the stiffness of the springs. You can calculate the required stiffness analytically, but
you can do differently and provide the solver with the opportunity to select them
in the process of a computational experiment. To do this, we calculate the position
of stable equilibrium using the initial equations as well as was done in the previous
task, with fixed values of elongations: