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Methods to quantify the energy losses within linear motion devices that included flexural springs as the main suspension component were investigated. The methods were applied to a two-stroke free-piston linear engine alternator (LEA) as a case study that incorporated flexure springs to add stiffness to the mass-spring system. Use of flexure springs is an enabling mechanism for improving the efficiency and lifespan in linear applications e.g. linear engines and generators, cryocoolers, and linear Stirling engines. The energy loss due to vibrations and windage effects of flexure springs in a free piston LEA was investigated to quantify possible energy losses. A transient finite element solver was used to determine the effects of higher modes of vibration frequencies of the flexure arms at an operational frequency of 65 Hz. Also, a computational fluid dynamics (CFD) solver was used to determine the effects of drag force on the moving surfaces of flexures at high frequencies.