The single most important thing when it comes to Simple Harmonic Motion (SHM), is the fact that acceleration is always directly proportional to displacement, and directed towards the centre point of equilibrium.
ie. acceleration (proportional to) -displacement
Also, it should be noted that a pendulum does not itself execute SHM. Only when you take a projection of the motion, in the plane generated by the equilibrial line of the motion, and the line perpendicular to this line, and also perpendicular to the motion of the pendulum... only then will the bottom of the pendulum appear to be executing SHM! In simple terms, if you have a pendulum on a string, and shine a light onto it sideways and place a screen behind, the shadow of the mass on your screen will appear to be executing SHM, going up and down, while the string appears to stay in the same place, only getting longer and shorter, as if by magic.
/msg me if you know the ascii code for the proportianlity sign. I couldnt find anything.