example 6.6 p.109

#a

gs = 1/((s + ζ ωn)^2 + q^2)

gt = InverseLaplaceTransform[gs, s, t]

#b

1 - (E^(-t ζ ωn)) Cos[
          q t] - (((E^(-t ζ ωn)) ζ ωn Sin[q t])/q)

st = 
      InverseLaplaceTransform[gs/s, s, t]  /. 
        (q^3) + q (ζ^2) ω(n^2) ->  
          q ωn^2

Simplify[
      st - (1 - (E^(-t ζ ωn)) Cos[
                  q t] - (((E^(-t ζ ωn)) ζ ωn Sin[q t])/q))/ωn^2]