eq = {x''[t] == -k*(x[t] - r[t]*Cos[theta]),
   r''[t] == -k*(r[t] - x[t]*Cos[theta])};

theta = Pi/4; k = 1;
ic = {x[0] == 1, r[0] == 0, x'[0] == 0, r'[0] == 0};
sol = NDSolve[{eq, ic}, {x, r}, {t, 0, 20}]

lst = Table[
   Graphics[{{Line[{{-1, 0}, {1, 0}}],
      Line[{{-Cos[theta], -Sin[theta]}, {Cos[theta],
         Sin[theta]}}]}, {Green,
      Line[{{x[t], 0}, {r[t]*Cos[theta], r[t]*Sin[theta]}} /.
        sol]}, {Red, PointSize[.05],  Point[{x[t], 0} /. sol],
      Point[{r[t]*Cos[theta], r[t]*Sin[theta]} /. sol]}}], {t, 0,
    10, .1}];

 ListAnimate[lst]