Clear[r, r1, L1, L2, L3, L4, L5, L6, L7, L8, L9, 
      L10]
r[t_] := (E^(-(t/3)))*
        Sin[t]
L1[t_] := 
      Show[Graphics[{RGBColor[0, 0, 1], Thickness[0.007], 
            Line[{{0, r[t]}, {0, -0.05 + r[t]}}]}], 
        DisplayFunction -> Identity]
L2[t_] := 
      Show[Graphics[{RGBColor[0, 0, 1], Thickness[0.007], 
            Line[{{0, -0.05 + r[t]}, {0.5, -0.1 + (11/12)*r[t]}}]}], 
        DisplayFunction -> Identity]
L3[t_] := 
      Show[Graphics[{RGBColor[0, 0, 1], Thickness[0.007], 
            Line[{{0.5, -0.1 + (11/12)*r[t]}, {-0.5, -0.2 + 
                    (9/12)*r[t]}}]}], 
        DisplayFunction -> Identity]
L4[t_] := 
      Show[Graphics[{RGBColor[0, 0, 1], Thickness[0.007], 
            Line[{{-0.5, -0.2 + (9/12)*r[t]}, {0.5, -0.3 + 
                    (7/12)*r[t]}}]}], 
        DisplayFunction -> Identity]
L5[t_] := 
      Show[Graphics[{RGBColor[0, 0, 1], Thickness[0.007], 
            Line[{{0.5, -0.3 + (7/12)*r[t]}, {-0.5, -0.4 + 
                    (5/12)*r[t]}}]}], 
        DisplayFunction -> Identity]
L6[t_] := 
      Show[Graphics[{RGBColor[0, 0, 1], Thickness[0.007], 
            Line[{{-0.5, -0.4 + (5/12)*r[t]}, {0.5, -0.5 + 
                    (3/12)*r[t]}}]}], 
        DisplayFunction -> Identity]
L7[t_] := 
      Show[Graphics[{RGBColor[0, 0, 1], Thickness[0.007], 
            Line[{{0.5, -0.5 + (3/12)*r[t]}, {-0.5, -0.6 + 
                    (1/12)*r[t]}}]}], 
        DisplayFunction -> Identity]
L8[t_] := 
      Show[Graphics[{RGBColor[0, 0, 1], Thickness[0.007], 
            Line[{{-0.5, -0.6 + (1/12)*r[t]}, {0.5, -0.65}}]}], 
        DisplayFunction -> Identity]
L9[t_] := 
      Show[Graphics[{RGBColor[0, 0, 1], Thickness[0.007], 
            Line[{{0.5, -0.65}, {-0.5, -0.7}}]}], 
        DisplayFunction -> Identity]
L10[t_] := 
      Show[Graphics[{RGBColor[0, 0, 1], Thickness[0.007], 
            Line[{{-0.5, -0.7}, {0.5, -0.72}}]}], 
        DisplayFunction -> Identity]
Table[
      Show[L1[t], L2[t], L3[t], L4[t], L5[t], L6[t], L7[t], L8[t], L9[t], 
        L10[t], PlotRange -> {{-3, 3}, {-1, 1}}, 
        DisplayFunction -> $DisplayFunction], {t, 0, 10, 
        0.1}]