This paper considers three dynamic systems composed of a mathematical pendulum suspended on a sliding body subjected to harmonic excitation. A comparative dynamic analysis of the studied parametric mutations of the rigid pendulum with inertial suspension point and damping was performed. The examined system with parametric mutations is solved numerically, where phase planes and Poincaré maps were used to observe the system response. Lyapunov exponents were computed in two ways to classify the dynamic behavior at relatively early stage of forced responses using two proven methods. The results show that with some parameters three systems exhibit a very similar dynamic behavior, i.e., quasi-periodic and even chaotic motions. Math. Comput. Appl. 2019, 24, 90 2 of 15 the full spectrum of Lyapunov exponents is presented in [3], the calculation of the largest Lyapunov exponent is given in [5,6], and the determination of the spectrum of Lyapunov exponents can be found in [7].From a practical point of view, Lyapunov exponents are used in various fields of science, such as: rotor systems [8], electricity systems [9], aerodynamics [10]. The Parametric Pendulum and Its Mutations