From the graph presented; angle versus time, it is evident that when the angle of displacement is increased, the periodic interval is reduced for a constant length if the string. This proportionality is directly varying.
In general, the swinging pendulum portrays a consistency in the changes involving kinetic, potential and gravitational potential energies. This can be summed serially as potential energy to kinetic energy then back to kinetic energy. This is when the pendulum is released from a height above the reference point level. At the instance the bob (mass) is released, it has an initial energy potential in nature. This is followed by gradual changes in the kinetic energies when at the minimum of the reference point; a maximum kinetic energy is attained. At this point, the swinging mass has its maximum velocity v, which is the converse for the point of zero (0) potential energy for the system in question. There are two maxima heights in respect of the reference position for the system. At these points, the system depicts its maxima potential energies which can as well be stated as minimum kinetic energy for the system.
A graph of kinetic energy versus time is a sinusoidal curve. This is the same for the case of potential energy. However the two curves are completely out of phase. This is due to the corresponding changes between kinetic to potential energy. This is evident in the total energy curve as a function of time; whose curve is straight. This is a true confirmation of the law of conservation of energy which can also be stated as “energy can neither be created nor destroyed, but rather conserved.”
For the pendulum, the reference level point to measure the y-coordinate location is at the mid-point between the two maxima levels of displacement of the pendulum. At equilibrium, the pendulum is at rest when it is at this point.
If the reference level is changed to where the rotary motion is, it would mean the length L is