The Lagrange-equation-based method (LEBM) is a general-purposed approach to determine the ordinary differential equations (ODEs) for a dynamic system; however, this procedure is daunting for undergraduate students. We show that this complicated task can be simplified significantly for the case of conservative scleronomous systems vibrating at low amplitude, which are encountered frequently in both textbooks and engineering practice. The ODEs for such systems are dictated by the mass and stiffness matrices. Both matrices can be determined from the quadric terms of Taylor's series of energy expressions expanded around the system's balanced configuration. This idea is illustrated by two examples.
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