Movimento de um pêndulo amortecido

Clear[θ,t]

L = 1.0;
g = 10.0;
λ = 0.2;
sol = NDSolveValue[{θ''[t] + (g/L)Sin[θ[t]]+ λ θ'[t]==0,θ[0]==π/3,θ'[0]==0},θ[t],{t,0,tf=40}];
pos[θ_]:={Cos[sol-π/2],Sin[sol-π/2]};
rhat[θ_]:=  {Cos[sol-π/2],Sin[sol-π/2]};
θhat[θ_]:=  {-Sin[sol-π/2],Cos[sol-π/2]};

Plot[sol,{t,0,tf},
FrameLabel->{"t","θ(t)"}
]

x(t) = r cos(θ(t))
y(t) = r sin(θ(t))

Animate[Graphics[{
Line[{{-1,0},{1,0}}],
Line[{{0,0},pos[sol]}],
Blue,PointSize[Large],
Point[pos[sol]],
Dashed,Black,
Line[{{0,0},{0,-1.3}}]
}/.t->tt],{tt,0,tf},AnimationRate->2]

Animate[Graphics[{
Line[{{-1,0},{1,0}}],
Line[{{0,0},pos[sol]}],
Blue,PointSize[Large],
Point[pos[sol]],
Red,
Arrow[{pos[sol],pos[sol]+0.25rhat[sol]}],
Arrow[{pos[sol],pos[sol]+0.25θhat[sol]}],
Dashed,Black,
Line[{{0,0},{0,-1.3}}],
Dotted,
Circle[{0,0},1],
Text[Style["(OverHat[r])(t)",Red,20],1.4pos[sol]],
Text[Style["(OverHat[θ])(t)",Red,20],pos[sol]+0.35 θhat[sol]]
}/.t->tt,
PlotRange->{{-1.3,1.3},{-1.5,0.3}},
ImageSize->400,
PlotLabel->Style["Os vetores (OverHat[r])(t) e (OverHat[θ])(t)",Bold,20]
],{tt,0,tf},AnimationRate->.05]

versor = vetor unitário

(OverHat[r])(t)  = cosθ(t) (OverHat[i])+ sin θ(t) (OverHat[j])
(OverHat[θ])(t) = -sinθ(t) (OverHat[i])+ cosθ(t)(OverHat[j])

Animate[Graphics[{
Line[{{-1,0},{1,0}}],
Line[{{0,0},pos[sol]}],
Blue,PointSize[Large],
Point[pos[sol]],
green,
Arrow[{pos[sol],pos[sol]+0.2D[pos[sol],t]}],
Dashed,Black,
Line[{{0,0},{0,-1.3}}],
Dotted,
Circle[{0,0},1],
Text[Style["(Overscript[v, ->])(t)",green,20],1.15pos[sol]],
}/.t->tt,
PlotRange->{{-1.3,1.3},{-1.5,0.3}},
ImageSize->400,
PlotLabel->Style["Vetor velocidade (Overscript[v, ->])(t)",Bold,20]
],{tt,0,tf},AnimationRate->.2]

(Overscript[v, ->])(t) = r ((dθ)/dt) (OverHat[θ])(t) =  r ω(t) (OverHat[θ])(t)

Animate[Graphics[{
Line[{{-1,0},{1,0}}],
Line[{{0,0},pos[sol]}],
Blue,PointSize[Large],
Point[pos[sol]],
green,
(* Full acceleration *)Arrow[{pos[sol],pos[sol]+0.1D[pos[sol],t,t] }],
Red,
Arrow[{pos[sol],pos[sol]+0.1D[sol,t,t]θhat[sol]}],
blue,
Arrow[{pos[sol],pos[sol]-0.1((D[sol,t])^2)rhat[sol]}],

Dashed,Black,
Line[{{0,0},{0,-1.3}}],
Dotted,
Circle[{0,0},1],
Text[Style["(Overscript[a, ->])(t)",green,20],1.2(pos[sol]+0.1D[pos[sol],t,t])],
Text[Style["(Subscript[a, T])(t)",red,20],1.1(pos[sol]+0.1D[sol,t,t]θhat[sol])],
Text[Style["(Subscript[a, cent.])(t)",blue,20],0.8(pos[sol]-0.1((D[sol,t])^2)rhat[sol])]
}/.t->tt,
PlotRange->{{-1.3,1.3},{-1.5,0.3}},
ImageSize->400,
PlotLabel->Style["Vetor aceleração (Overscript[a, ->])(t)",Bold,20]
],{tt,0,5},AnimationRate->.05]

(Overscript[a, ->])(t) = r ((dω)/dt) (OverHat[θ])(t) - r (ω^2)(t) (OverHat[r])(t)