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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);