Hi everyone. I've started to use Wolfram Mathematica recently and I was trying to solve a system of coupled differential equations. The second of these equations presents a function dependent by the "t " variable and defined in a specific range of values, since it presents points of singularity. Unfortunately, even by defining all the intervals where such function is defined, it seems like the solver keeps considering these points belonging to the interval, giving the message "ERROR: infinite expression 1/0 encountered".
I'll write in the following lines what I've put in the program:
m1 = 50; (*kg*)
m2 = 8; (*kg*)
k1 = 4000; (*N/m*)
k2 = 180000; (*N/m*)
c = 150; (*Ns/m*)
v = 2.78; (*m/s*)
z = 2.71828;
H0 = 0.09; (*m*)
L0 = 0.27; (*m*)
ClearAll[h];
h[t_] :=
Piecewise[{{0,
t <= 1}, {Unevaluated[
z*H0*Exp[-1/(1 - (2*v*(t - 1)/L0 - 1)^2)]],
1 < t < 1 + L0/v}, {0, t >= 1 + L0/v}}]; // FullSimplify
sol = NDSolve[{m1 x''[t] + c (x'[t] - y'[t]) + k1 (x[t] - y[t]) ==
0, m2 y''[t] + c (y'[t] - x'[t]) + k1 (y[t] - x[t]) +
k2 (y[t] - h[t]) == 0, x[0] == 0, x'[0] == 0, y[0] == 0,
y'[0] == 0}, {x[t], y[t]}, {t, 0, 4.5}];
Plot[Evaluate[{x[t], y[t]} /. sol], {t, 0, 4.5},
PlotLabels -> {"x1(t)", "x2(t)"},
AxesLabel -> {"time, s", "displacement, m"},
PlotLegends -> "Expressions", PlotRange -> All,
Exclusions -> "Singularities"]
I've already tried to check in another discussions about this topic, but the problem sill persists. So the final question is, how can I solve the error here presented? Thank you!
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