Please explain what the phase constant a phase angle is in terms of a simple pendulum..?

Any motion that repeats itself at regular intervals is called harmonic motion. A particle experiences a simple harmonics motion if its displacement from the origin as function of time is given by

 

 

 

where x_m, [omega] and [phi] are constants, independent of time. The quantity x_m is called the amplitude of the motion and is the maximum displacement of the mass. The time-varying quantity ([omega]t + [phi]) is called the phase of the motion and [phi] is called thephase constant. The phase constant is determined by the initial conditions. The angular frequency [omega] is a characteristic of the system, and does not depend on the initial conditions. The unit of angular frequency is rad/s. The period T of the motion is defined as the time required to complete one oscillation.