Clear[n, l, dt, q, t, θ, ω]
Tt = {};
n = 4000;
l = 9.8;
g = 9.8;
dt = 0.02;
q = 0.5;
t = 0;
 ω = 0;
 θ = 0.2;
F = 1.35;
Ω = 2/3;
For[i = 1, 
      i ≤ 
        n, i++, 
ω = ω - (g/l)*
            Sin[θ]*dt - q*ω*dt + 
          F*Sin[Ω*t]*
            dt; 
θ = θ + ω*
            dt; 
If [θ > 
          Pi, θ = θ - 
            2.0*Pi]; 
If [θ < -Pi, θ = θ + 2.0*Pi]; 
t = 
        t + dt; 
AppendTo[
        Tt, {t, θ}];
]
ListPlot[Tt, PlotJoined -> True, AxesLabel -> {T, theta}, 
        PlotRange -> {-5, 5}];

Clear[n, l, dt, q, t, θ, ω]
Tt = {};
n = 4000;
l = 9.8;
g = 9.8;
dt = 0.02;
q = 0.6;
t = 0;
 ω = 0;
 θ = 0.2;
F = 1.44;
Ω = 2/3;
For[i = 1, 
      i ≤ 
        n, i++, 
ω = ω - (g/l)*
            Sin[θ]*dt - q*ω*dt + 
          F*Sin[Ω*t]*
            dt; 
θ = θ + ω*
            dt; 
If [θ > 
          Pi, θ = θ - 
            2.0*Pi]; 
If [θ < -Pi, θ = θ + 2.0*Pi]; 
t = 
        t + dt; 
AppendTo[
        Tt, {t, θ}];
]
ListPlot[Tt, AxesLabel -> {T, theta}, PlotJoined -> True, 
        PlotRange -> {-3, 3}];

Clear[n, l, dt, q, t, θ, ω]
Tt = {};
n = 4000;
l = 9.8;
g = 9.8;
dt = 0.02;
q = 0.8;
t = 0;
 ω = 0;
 θ = 0.2;
F = 1.465;
Ω = 1/6;
For[i = 1, 
      i ≤ 
        n, i++, 
ω = ω - (g/l)*
            Sin[θ]*dt - q*ω*dt + 
          F*Sin[Ω*t]*
            dt; 
θ = θ + ω*
            dt; 
If [θ > 
          Pi, θ = θ - 
            2.0*Pi]; 
If [θ < -Pi, θ = θ + 2.0*Pi]; 
t = 
        t + dt; 
AppendTo[
        Tt, {t, θ}];
]
ListPlot[Tt, PlotJoined -> True, AxesLabel -> {T, theta}, 
        PlotRange -> {-3, 3}];