m := 1.33;
r := 3.33;
k := 6.33;
with(inttrans);
assume(0 < T);
Y := (2 - 2*exp(-T*s))/(m*s^3 + r*s^2 + k*s);
y := invlaplace(Y, s, t);
y14 := subs(t = 14, y);
Toff := fsolve(y14 = 0, T, 12.5 .. 14);
Toff := 12.77874798
yt := subs(T = Toff, y);
ytp := diff(yt, t);
plot([yt, ytp], t = 0 .. 20, color = [red, blue], title = `\`Solution of\n first part 0-20t: `*`Sarwar, 30333`*`);\n plot([yt,ytp],t=12..15,color=[red,blue],title=\`Solution of\n first part 12-15t: Sarwar, 30333`);
y2 := yt + invlaplace(W*exp(-15*s)/(m*s^2 + r*s + k), s, t);