I am trying to define a following function (which is a convolution integral)
force[τ_] :=
Piecewise[{
{F0 τ/(t1/2), 0 <= τ < t1/2},
{2 F0 (1 - τ/t1), t1/2 <= τ < t1},
{0, t1 <= τ}}]
x1[t_] :=
Integrate[
1/m force[τ] 1/ω0 Sin[ω0 (t - τ)], {τ, 0, t},
Assumptions -> {0 <= t, t <= t1/2}]
F0 = 31.6*1000 (*N*);
t1 = 0.0109 (*s*);
m = 4200(*kg*);
k = 40000;
ω0 = Sqrt[k/m];
xprvi = Plot[x1[t], {t, 0, t1/2}, PlotRange -> All]
Yet this doesn't work at all. Not even close. The output is empty. I thought this is a correct definition, yet it looks like I was wrong.
:=
with=
in the definition forx1
(after clearing all previous definitions)? $\endgroup$