With many physical applications already on the table, in this chapter, we return to some of the simplified ones and re-complexify them.These problems require more sophisticated, and incomplete, solutions.Instead of finding the position of the bob for the simple pendulum, we find the period of motion for the ``real" pendulum.Instead of the classical harmonic oscillator, with its familiar solution, we study the period of the relativistic harmonic oscillator, and find that in the high energy limit, a mass attached to a spring behaves very differently from its non-relativistic counterpart.