(* Solution to Problem Set 9.
At the Mathematica prompt, type
<< ans9.math
*)

(* The Green's function *)
G[dt_] := 1/nu E^(-e dt/2) Sin[nu dt];
(*
G[dt_] := 1/nu E^(-e dt/2) Sinh[nu dt];
*)

(* The forcing function *)
f[t_] := Sin[q t];

(* The solution *)
u = Integrate[ G[t-tp] f[tp] , {tp,0,t}];

(* The solution after a long time *)
uc = Coefficient[u, Cos[q t]];
us = Coefficient[u, Sin[q t]];
ulong = Together[ uc Cos[q t] + us Sin[q t] ];

(* The square of the amplitude after a long time *)
asq = Factor[ uc^2 + us^2 ];

(* Print out TeX version of the solution *)
u // TeXForm