documentclass{article}

usepackage{tikz}
begin{document}
begin{tikzpicture}

 draw[domain=0:720,smooth,variable=t]
plot ({1.5*sin(t)},0.8*t/360,{1.5*cos(t)});
draw[->] (0,0,0) --( 2,0,0) node[above]{y};
draw[->] (0,0,0) --( 0,2,0) node[right]{z};
draw[->] (0,0,0) --( 0,0,2,) node[above]{x};
end{tikzpicture}
hspace{3em}
begin{tikzpicture}

 draw[domain=0:20,smooth,variable=t,samples=200]
plot ({t r:3*exp(-0.1*t)});
draw[->] (0,0,0) --( 4,0) node[above]{x};
draw[->] (0,0,0) --( 0,4) node[right]{y};

end{tikzpicture}

end{document}

documentclass[a4paper, pdf, svgnames]{article}
usepackage[utf8]{inputenc}
usepackage[T1]{fontenc}
usepackage[f]{esvect}
pagestyle{empty}
usepackage{pstricks-add}
deflocalbasis{psline{<->}(1,0)(0,0)(0,1)}

begin{document}

small
psset{plotpoints=500, algebraic, arrowinset=0.2, labelsep=3pt}
begin{pspicture}
psaxes[labels=none, ticks=none]{->}(0,0)(-4.5,-3)(6,5)
radians
pnodes(0,0){O}( 4.524; 0.5){M}
uput{6pt}[u](M){,,M}
rput(O){localbasis}uput{3pt}[dr](O){$ O $}uput[d](1,0){{$ vv*{e}{!!x }$}}uput{2pt}[dl](0,0.9){{$ vv*{e}{!!y} $}}
psplot[polarplot, arrows=*-, linecolor=VioletRed, linewidth=1.2pt, dotsize=2.5pt]{0}{25}{5*EXP(-x/5)}
uput[d](5,0){$ mathrm M(t = 0) $}
rput{0.5}(M){localbasis}
pcline{-o}(O)(M)naput {$ r $}
psarc[linewidth 0.5pt]{->}{2.2}{0}{0.5}uput[r](2.2; 0.3){ $ θ $}
pnode(5.7; 0.5){I}rput[I](I){$vv*{e}{!!r}$}
psRelNodeVar(M )( I)( 1;1.57){J}rput[B](J){$vv*{e}{!!θ}$}
end{pspicture}

end{document}

documentclass[a4paper, pdf, x11names]{article}
usepackage[utf8]{inputenc}
usepackage[T1]{fontenc}
usepackage{MinionPro}
usepackage[f]{esvect}
pagestyle{empty}
usepackage{pstricks-add, pst-3dplot}
deflocalbasis{psline{<->}(1,0)(0,0)(0,1)}
def\M{6*pstPI1}
begin{document}

small
psset{xPlotpoints = 500, plotstyle=curve, linecolor = DarkSeaGreen3, algebraic, arrowinset=0.2, labelsep=3pt}
begin{pspicture}(-4,-2.5)(4,5.5)
pstThreeDCoor[zMax=5.5, yMax=5, xMax=5, linewidth=0.6pt, linecolor=Coral1]
psset{linewidth=1.5pt}
parametricplotThreeD(0, 20){% radiant % 18.86
2.5 * cos(t) | 2.5 * sin(t) | t/5}
psset{border=1.5pt}
parametricplotThreeD(0.1, 4){% radiant %
2.5 * cos(t) | 2.5 * sin(t) | t/5}
parametricplotThreeD(5.240, 8.38){% radiant %
2.5 * cos(t) | 2.5 * sin(t) | t/5}
parametricplotThreeD(11.52, 14.66){% radiant %
2.5 * cos(t) | 2.5 * sin(t) | t/5}
parametricplotThreeD(17.80, 20.5){% radiant %
2.5 * cos(t) | 2.5 * sin(t) | t/5}
psset{linewidth=0.6pt, linecolor=Coral1}
pstThreeDLine(0,0,2)(0,0,2.4)
pstThreeDLine(0,0,3.3)(0,0,5.0)
pstThreeDLine[linecolor=black, border = 0pt]{-> }(0,0,0)(0, 2.5, 2.79)
uput[u](1.7,1.6){ $ M $}uput[-120](0,0){$ O $}
pstThreeDDot[linecolor = DarkSeaGreen3](0, 2.5, 2.83)
pstThreeDDot(0,0,0)
end{pspicture}

end{document}

documentclass[tikz]{standalone}
usepackage{tikz,bm}
usetikzlibrary{angles,arrows,calc,quotes}
begin{document}
begin{tikzpicture}[
  thick,>=stealth',
  declare function = {
    logx(a,b,r) = a*exp(-b*r)*cos(deg(r));
    logy(a,b,r) = a*exp(-b*r)*sin(deg(r));
  },
  point/.style={draw,thick,circle,inner sep=1pt,label={#1}},
  plot/.style={blue,smooth,samples=100}
  ]
  % Spiral parameters
  defa{5}
  defb{.2}
  % Axes
  draw[->] (-4.5,0) -- (6,0) coordinate[label={below:$x$}] (A);
  draw[->] (0,-3) -- (0,5) node[left] {$y$};
  % Spiral
  draw[plot] plot[domain=0:25] ({logx(a,b,x)},{logy(a,b,x)});
  % Points M, O and M(t=0)
  coordinate[label={below right:$O$}] (B) at (0,0);
  node[point={above:$M$}] (C) at ({logx(a,b,.7)},{logy(a,b,.7)}) {};
  node[below] at ({logx(a,b,0)},{logy(a,b,0)}) {$M(t=0)$};
  % Angle
  draw pic[->,draw,"$varphi$",angle radius=1.5cm] {angle};
  % Unit vectors
  draw[->] (B) -- ($(B)!1.3!(C)$)       node[below right] {$bm{e}_r$};
  draw[->] (C) -- ($(C)!-1.5cm!90:(B)$) node[above right] {$bm{e}_theta$};
  draw[->] (B) -- +(1,0)                node[below]       {$bm{e}_x$};
  draw[->] (B) -- +(0,1)                node[left]        {$bm{e}_y$};
end{tikzpicture}

begin{tikzpicture}[
  x={(-.707cm,-.353cm)},y={(1cm,0cm)},z={(0cm,1cm)},
  thick,>=stealth',
  plot/.style={blue,smooth,samples=100}
  ]
  % Origin and axes
  coordinate[label={above left:$O$}] (O) at (0,0,0);
  draw[->] (O) -- (2,0,0) node[above left] {$x$};
  draw[->] (O) -- (0,2,0) node[above] {$y$};
  draw[->] (O) -- (0,0,4) node[right] {$z$};
  % Plot
  draw[plot] plot[domain=0:16] ({cos(deg(x))},{sin(deg(x))},{.25*x});
  % Arrow to M
  draw[->] (O) -- ({cos(deg(8))},{sin(deg(8))},2) node[right] {$M$};
end{tikzpicture}
end{document}

% pdflatex
documentclass[margin=2mm]{standalone}
usepackage{tikz}
usepackage{pgfplots}
pgfplotsset{compat=newest}

begin{document}
begin{tikzpicture}
       pgfmathdeclarefunction{F}{3}{pgfmathparse{#1* exp(#2*#3)}}
begin{axis}
        [
        smooth, grid=both,minor tick num=1,
        xlabel=$x$,ylabel=$y$,
        tick align=inside,
        samples=1000,
        samples y=0,
        ]

        addplot [solid, thick, data cs=polarrad, domain=0:10*pi] {F(5,-0.1,x)};
end{axis}
end{tikzpicture}
~
begin{tikzpicture}
       pgfmathdeclarefunction{F}{3}{pgfmathparse{#1* exp(#2*#3)}}
begin{axis}
        [smooth, grid=both,minor tick num=1,
        xlabel=$x$,ylabel=$y$,zlabel=$z$,
        samples=1000,
        samples y=0,
        ]

        addplot3+
        [solid, thick, black,
        mark=none,
        thick,
        domain=0:10*pi,
        ]
        ({F(5,-0.1,x)*cos(deg(x))},{F(5,-0.1,x)*sin(deg(x))},{F(5,-0.1,x)});
end{axis}
end{tikzpicture}
end{document}