On the Stability of a Differential Equation With Application to the Vibrations of a Particle in the Plane

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Abstract
The stability of the equation Z¨ + f(t)Z = 0, where f(t) = (δ − ε cos2t)/(1 − ε cos2t), is studied by using Floquet theory, Fourier analysis and perturbations. The results are used to study the stability of the vibrations of a particle constrained to a plane and restrained by two identical linear springs with initial stress.