Nonlinear dynamical systems, being more of a realistic representation
of nature, could exhibit a somewhat complex behavior. Their analysis r
equires a thorough investigation into the solution of the governing di
fferential equations. In this paper, a class of third order nonlinear
differential equations has been analyzed. An attempt has been made to
obtain sufficient conditions in order to guarantee the existence of pe
riodic solutions. The results obtained from this analysis are shown to
be beneficial when studying the steady-state response of nonlinear dy
namical systems. In order to obtain the periodic solutions for any for
m of third order differential equations, a computer program has been d
eveloped on the basis of the fourth order Runge-Kutta method together
with the Newton-Raphson algorithm. Results obtained from the computer
simulation model confirmed the validity of the mathematical approach p
resented for these sufficient conditions.