Mathematical Pendulum with Random Force

Starting the pendulum in the upper position it should stay there, because all forces cancel. In reality it eventually falls to one side, due to the influence of tiny random forces. Such forces are included in this simulation. Restart the simulation several times and compare the resulting movements of the pendulum. Repeat this experiment using the MathPendulum applet. What happens?

Let the simulation run for a longer time and write down a 0 or 1 for each period, according to a swing to the left or right. Is the resulting sequence random? What happens, if one changes the amplitude A of the random force?

With increasing values of A the simulation gets slower, until it almost freezes. This is due to the behaviour of the solver: It tries to cope with large changes in the force by decreasing the simulation stepsize. For ordinary forces this leads to an almost constant force during one time step, making the simulation more accurate. But here the random values always jump erratically, thereby giving the solver a hard time.