For small amplitudes the oscillation period, T, of a pendulum only depends
on the length, L, and on the gravitational acceleration, g, and is given
by the following formula:
            ┌────────────────────────────┐
            │  T = 2 * pi * sqrt( L/g )  │
            └────────────────────────────┘         where  pi = 3.14159...

The derivation of this formula requires some calculus and concepts such as
moment of inertia, angular momentum etc.  But you can get a good idea of
how it works by just knowing that  ** acceleration = force/mass **. The
force that drives the motion is the tangential component of the weight. The
radial component is canceled by the tension of the string.  Notice that the
tangential component always points towards the equilibrium position and
thus accelerates the pendulum while moving towards the middle and
decelerates it while moving away.

Why doesn't the period depend on the mass?  See what happens when you
change the mass by pressing F2. Notice that the force changes in the same
proportion as the mass. Therefore the   acceleration = force/mass   
(long tangential arrow)  will be the same as before at any point. Since the
acceleration is what causes the velocity to build up or to decrease; the
velocity will also be the same as before at any point, the motion will not
change and the period will remain the same.
