On thin elastic rods with quickly changing periodic properties

The flat thin elastic rod with free form represented by a periodic curve is considered. It is shown, that in a limit, with constant forces and moments enclosed and indefinitely growth of frequency of a function that describes the free form, the equilibrium form of a rod aspires to the one of a thin rectilinear rod. According to Kirhgoff analogy this task can be interpreted as a movement of a mathematical pendulum with a quickly varying periodic revolting force enclosed. The solution of a considered task is carried out within the framework of substantiating the applicability of modeling the spatial forms of ring DNA molecules by a thin rectilinear elastic rod.