para = {U ->  UnitStep, h ->  Exp[-s]}

Q 5.5 (1)  p.99

fs = 4/s - h/s^2 /. para

ft = InverseLaplaceTransform[fs, s, t]
Simplify[4 - (t - 1) U[t - 1] - ft /. para]

Plot[ft, {t, 0, 6}, AspectRatio ->  0.2]

Q 5.5 (2)  p.99

fs = -(s + 10)/(s^2 - s - 2)

ft = InverseLaplaceTransform[fs, s, t]

Plot[ft, {t, 0, 1}, AspectRatio ->  0.2]

Q 5.5 (3)  p.99

fs = (1 - 7 s)/(s - 3)/(s - 1)/(s + 
            2)

ft = InverseLaplaceTransform[fs, s, t]

Plot[ft, {t, 0, 1}, AspectRatio ->  0.2]

Q 5.5 (4)  p.99

fs = 1/(s + 1)^2

ft = InverseLaplaceTransform[fs, s, t]

Plot[ft, {t, 0, 10}, AspectRatio ->  0.2]

Q 5.5 (5)  p.99

fs = 3/(s^2 + 6 s + 18)

ft = 
      Simplify[ExpToTrig[
          InverseLaplaceTransform[fs, s, t]]]
Simplify[Exp[-3 t] Sin[3 t] - %]

Plot[ft, {t, 0, 2}, AspectRatio ->  0.2, 
      PlotRange ->  {0, 0.5}]