![]() ![]() ![]() ![]() Rather than creating an automated engineering computation worksheet, MathWorks chose to create a “high-level” programming language with the functions and functionality needed for engineering and scientific computing. MathWorks, the developer of MATLAB took a different approach from Mathsoft. Mathcad worksheets are evaluated automatically from top to bottom, left to right when any change is made. The regions within the worksheet can be dragged around, resized, copied, and edited. What the user sees is actually a graphical interface defined by user created “regions” or objects that support mathematics, graphics, or text. A Mathcad “worksheet” presents equations in as close to standard mathematical notation as possible. Mathsoft, the originator of Mathcad, chose to develop software which emulated the mixture of mathematics, graphics, and text, which typifies manual engineering calculations. Two Massachusetts companies targeted engineering and scientific computation with radically different approaches. In the early 1980s, shortly after personal computers were introduced, there was a flurry of activity to develop software for the emerging market. This process is experimental and the keywords may be updated as the learning algorithm improves. These keywords were added by machine and not by the authors. The chapter’s appendix introduces Mathcad and MATLAB to plot the solutions or response functions. The Laplace transformation transforms differential equations into algebraic equations, which can be expressed as multiplicative dynamic operators called transfer functions. Complex numbers, complex exponentials, and Euler’s equations simplify the solution and interpretation of the response of oscillatory systems. Systems with two or more independent energy storage elements yield differential system equations which may describe oscillations or vibrations. The method of undetermined coefficients superposes or sums the response of a system into the natural or homogeneous response of the system to a disturbance to its energetic equilibrium, and the steady-state or particular response to each input driving the system. We simplify, or linearize, the individual energetic element equations, in order to derive a system equation which is an ordinary differential equation with constant coefficients, a form which we can solve for the output or response function. Differential system equations describe the dynamic relationship between an input driving the system, and one of the power variables within the energetic system. ![]()
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