On the linear theory of the elastic pendulum

A harmonic oscillator in a gravitational field, such as a weight on a spring, sometimes exhibits loss of lateral stability due to parametric resonance. The resulting horizontal, or pendulum oscillation is analysed by means of a locus line drawn in the Ince-Strutt stability chart of the respective Mathieu equation, to determine graphically the range of mass leading to instability for a particular amplitude of the initially vertical oscillation and the corresponding growth coefficient.