Lecture-1-2-Modeling, Computers, and Error

Lecture-1-2-Modeling - BME5020 2006 Fal Semester |Biomedical Engineering Wayne State University Modeling Computers and Error BME 5020 Computer and

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Unformatted text preview: BME5020 2006, Fal Semester |Biomedical Engineering, Wayne State University Modeling, Computers, and Error BME 5020 Computer and Mathematical Application in Bioengineering • Modeling • Programming • Errors © 2006 Jingwen Hu September 7, 2006 Contents Mathematical Model • Definition: a formulation or equation that expresses the essential features of a physical system or process in mathematical terms • Computers are great tools, however, without fundamental understanding of engineering problems, they will be useless. BME5020 2006, Fal Semester |Biomedical Engineering, Wayne State University Mathematical Model (cont’d) • A mathematical model is represented as a functional relationship of the form Dependent independent forcing Variable = f variables , parameters , functions • Dependent variable : Characteristic that usually reflects the state of the system • Independent variables : Dimensions such as time and space along which the systems behavior is being determined • Parameters : reflect the system’s properties or composition • Forcing functions : external influences acting upon the system BME5020 2006, Fal Semester |Biomedical Engineering, Wayne State University Example - Newton’s second law of motion • States that “ the time rate change of momentum of a body is equal to the resulting force acting on it .” • The model is formulated as F = m a F - net force acting on the body (N) m - mass of the object (kg) a - its acceleration (m/s 2 ) BME5020 2006, Fal Semester |Biomedical Engineering, Wayne State University Example - Newton’s second law of motion • Rewrite the Newton’s second law of motion as a = F / m • Where • a is the dependent variable reflecting the system’s behavior • F is the forcing function • m is a parameter representing a property of the system • No independent variable because we are not yet predicting how acceleration varies in time or space BME5020 2006, Fal Semester |Biomedical Engineering, Wayne State University Example - Newton’s second law of motion BME5020 2006, Fal Semester |Biomedical Engineering, Wayne State University • The above equation can be written as in differential equation form • A differential equation is an equation that defines a relationship between a function and one or more derivatives of that function. m F dt dv = Example - Modeling of a falling parachutist • A parachutist of mass 68.1 kg jumps out of a stationary hot air balloon. Assuming the drag coefficient is 12.5 kg/s, determine the terminal velocity. • To formulate this problem, one must first draw a free body diagram (FBD) BME5020 2006, Fal Semester |Biomedical Engineering, Wayne State University Example - Modeling of a falling parachutist • Free Body diagrams (FBD’s) are simplified vector representations of an object (the body) and all force vectors acting on the object. This body is free, because the diagram show the object without its surroundings; i.e. the body is “free” of its environment. surroundings; i....
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This note was uploaded on 04/04/2008 for the course BME 5020 taught by Professor King during the Fall '06 term at Wayne State University.

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Lecture-1-2-Modeling - BME5020 2006 Fal Semester |Biomedical Engineering Wayne State University Modeling Computers and Error BME 5020 Computer and

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