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...Applied engineering analysis slides for class teaching chapter application of second order differential equations in mechanical based on the book by tai ran hsu published john wiley sons isbn des learning objectives refresh solution methods typical homogeneous and non learned previous math courses learn to derive free vibration simple mass spring system with without damping effects nonhomogeneous forced systems use illustrate resonant estimate time rupture under equation predict amplitudes vibrating situation near physical consequences concept modal machines structures consequence structural failure modes review method ordinary we will techniques available solving at beginning this presented subsequent sections are generic effective form p du x dx a bu where b constants u may be obtained assuming emx which m is constant determined following procedure if assumed valid it must satisfy that demx mx e d because memx substitution above expressions into lead me expression cannot zero why thu...