The purpose of this study is to identify the nonlinear dynamics of the double torsion pendulum with planar friction and elastic barriers. The original experimental stand consists of a disk-shaped body that rotates freely on top of a forced column with a system of barriers limiting the torsional vibrations of the pendulum bodies that create an nonuniform planar rotational friction contact. Two beam springs form soft barriers modeled by Voigt elements that limit the angular displacement of one of the pendulum bodies—the disk, while the second limiting system, made of a much more rigid barrier, limits the movement of the pendulum’s second body. The dynamic behavior of the asymmetrical system of two degrees of freedom with discontinuities is identified with the use of the described strategy, numerical solutions of the derived mathematical model and the Nelder–Mead simplex algorithm. The actual measurement series and numerical solutions show a good similarity of the dynamical reaction of the mechanical system and its virtual analog.