Abstract: In this work, we focus on the mechanical system of a suspended picture frame. With both the Newtonian mechanics and Lagrangian analytical mechanics methods, we derive the equilibrium conditions of the system and the differential equations of two-degree-of-freedom small oscillations, discuss the existence conditions of normal frequencies. We also use Mathematica to numerically solve the differential equations, verifying the correctness of the relevant discussion results.

Key words: equilibrium state, small oscillations, Newtonian mechanics, analytical mechanics, numerical calculation