Nonlinear oscillation analysis of a pendulum wrapping on a cylinder

In this paper, the nonlinear oscillation of a pendulum wrapping and unwrapping on twocylindrical bases is studied, and an analytical solution is obtained using the multiple scales method. theequation of motion is derived based on an energy conservation technique. by applying the perturbationmethod to the differential equation, the nonlinear natural frequency of the system is calculated, alongwith its time response. analytical results are compared with numerical findings and good agreement isfound. the effect of large amplitude and radius of cylinders on system frequency is evaluated. the resultsindicate that as the radius of the cylinder increases, the system frequency is increased. also, it is illustratedthat initial amplitude plays a dual role in the frequency. as the initial amplitude increases up to a certainpoint, the frequency is increased, while by increasing it to higher values, the system frequency decreases.