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By Michael Spektor
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Extra info for Solving Engineering Problems in Dynamics
Sample text
5 Two springs act sequentially. 2) o where i = 1, 2, 3, …, n, and n is the number of springs. 5 shows a vibratory system with two springs that are sequentially attached to the mass. 3) where i = 1, 2, 3, …, n, and n is the number of links. In this text, when physical springs are not present, the mathematical models of motion use springs to represent the stiffness forces. 6 A combination of springs acting in parallel and in sequential order. coefficients K1 and K 2 that act in parallel and a pair of springs with stiffness coefficients K 3 and K 4 that act sequentially.
This methodology is based on converting a differential equation of motion from the time domain into a corresponding equation in the Laplace domain. After the conversion, the new Laplace domain equation is made up entirely of conventional algebraic expressions. Some of these expressions in the left side of this equation have the Laplace domain displacement function as multipliers. This displacement function represents the solution of the Laplace domain equation; the function should be factored out using regular algebraic procedures.
Pairs are identified by comparing their structures; no specific mathematical actions are necessary. Note that x ( t ) is the displacement as a function of the running time in the time domain whereas x ( l ) is the corresponding displacement function in the Laplace domain, with l is an independent variable complex value. You do not need to memorize the detailed basics of the Laplace Transform in order to use its methodology. Even though the fundamentals of the Laplace domain are presented in numerous publications, there is no need to get familiar with these fundamentals in order to comprehend the contents of this book and widely use the Laplace Transform to solve linear differential equations of motion.