the following test works for fixed parameter si:
test = Block[{si = 2},
k = si s^2 + 107 s/5 + 10 ((1 + s)^(-2) - 1) - 1/10;
cr = Chop[N[Solve[k == 0, s], 12]];
Wsa = Apart[(1 + s)^2/(si Product[s - (s /. cr[[i]]),
{i,4}])];
Wp[y_] := D[InverseLaplaceTransform[Wsa, s, x], x] /.x->
y];
Plot[Evaluate[Wp[x]], {x, 0, 16}]
Turning it to Manipulate results in infinite evaluation on 11.3, and messages General::ivar: 0.0003268571428571428` is not a valid variable. Help?
k = si s^2 + 107 s/5 + 10 ((1 + s)^(-2) - 1) - 1/10;
Manipulate[cr = Chop[N[Solve[k == 0, s], 12]];
Wsa = Apart[(1 + s)^2/(si Product[s - (s /. cr[[i]]), {i, 1, 4}])];
Wp[y_] := D[InverseLaplaceTransform[Wsa, s, x], x] /. x -> y;
Plot[Evaluate[Wp[x]] /. {si -> s2}, {x, 0, 16}], {{s2, 1, "s2"}, 1,
2, Appearance -> "Labeled"}]