F[t_] = Piecewise[{{Subscript[F, 0] t/(T/2), 
    0 <= t <= T/2}, {-Subscript[F, 0], T/2 <= t <= T}}]
Subscript[F, 0] = 268(*N*);
T=33921.8;
Plot[{F[t]}, {t, 0, T}, PlotRange -> All, 
 Frame -> True, FrameLabel -> {"t [s]", "M [Nm]"}, 
 BaseStyle -> {FontFamily -> "Courier New", FontSize -> 10}]
	
a0 = 2/T Integrate[F[t], {t, 0, T}, 
    Assumptions -> {T [Element] Reals, T > 0}];

aj[j_] = 2/
   T Integrate[Cos[j 2 Pi t/T] F[t], {t, 0, T/2}, 
    Assumptions -> {T [Element] Reals, T > 0}];

bj[j_] = 2/
   T Integrate[Sin[j 2 Pi t/T] F[t], {t, 0, T}, 
    Assumptions -> {T [Element] Reals, T > 0}];
	
x[t_, num_] := x0 + Sum[xa[t, j], {j, 1, num}] + Sum[xb[t, j], {j, 1, num}]
	
β[j_] = 1/
  Sqrt[(1 - ((j 2 Pi)/(T ω0))^2)^2 + (2 δ (
     j 2 Pi)/(T ω0))^2];

ϕ[j_] = 
  ArcTan[(1 - ((j 2 Pi )/(τ ω0))^2), (2 δ (
     j 2 Pi)/(τ ω0))];

x0 = a0/(2 ω0^2 Jn);
xa[t_, j_] := 
  aj[j]/(Jn ω0^2) β[j] Cos[j 2 Pi t/τ - ϕ[j]];
xb[t_, j_] := 
  bj[j]/(Jn ω0^2) β[j] Sin[j 2 Pi t/τ - ϕ[j]];
	
omegas={0.000154355, 0.00029819, 0.000421705, 0.000516481, 0.00057606}
	
diagM={{2964, 0, 0, 0, 0}, {0, 988, 0, 0, 0}, {0, 0, 741, 0, 0}, {0, 0, 0, 
  988, 0}, {0, 0, 0, 0, 2964}}
x[t_, num_] := 
 Table[x0[[i]] + Sum[xa[[i]], {j, 1, num}] + 
   Sum[xb[[i]], {j, 1, num}], {i, 1, 5}]

δ = 0.23;

x0 = Table[a0/(2 ω0^2 diagM[[i, i]]), {i, 1, 5}];

xa = Table[
   aj[j]/(diagM[[i, i]] omegas[[i]]^2) 1/
    Sqrt[(1 - ((j 2 Pi)/(T omegas[[i]]))^2)^2 + (2 δ (
       j 2 Pi)/(T omegas[[i]]))^2]
     Cos[j 2 Pi t/T - 
      ArcTan[(1 - ((j 2 Pi )/(T omegas[[i]]))^2), (2 δ (
         j 2 Pi)/(T omegas[[i]]))]], {i, 1, 5}];

xb = Table[
   bj[j]/(diagM[[i, i]] omegas[[i]]^2) 1/
    Sqrt[(1 - ((j 2 Pi)/(T omegas[[i]]))^2)^2 + (2 δ (
       j 2 Pi)/(T omegas[[i]]))^2]
     Sin[j 2 Pi t/T - 
      ArcTan[(1 - ((j 2 Pi )/(T omegas[[i]]))^2), (2 δ (
         j 2 Pi)/(T omegas[[i]]))]], {i, 1, 5}];