1. BY: MARIA FERNANDA VERGARA M. UNIVERSIDAD INDUSTRIAL DE SANTANDER
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3. f , , Reflects the system behavior These ones are dimensions, for example: time These ones tell us about system properties These ones are external influences that affect the system Dependent variable Independent variables parameters Forcing functions
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5. Express the hypotesis in terms of differential equations Solving the D.E. Showing model predictions If required, raise the complexity of the model or change the hypothesis Hypothesis Testing Getting solutions Mathematical formulation or equation
6. W F r Newton’s Second Law: Where: a is the dependent parameter F is the forcing function m is the parameter ¿Which is the terminal velocity of a free-falling body near the earth’s surface?
7. W F r Net Force: F r + W Fr = -c v W= mg Where and Drag Coefficient Solving, and taking into account that initial velocity is 0: Analytical or exact solution
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9. Source: CHAPRA,Steven C., Numerical Methods for Engineers. Mc Graw Hill Using Newtons law, but realizing that the time rate of change of velocity can be aproximated by: We can get a numerical solution for the same problem of the parachute:
10. Now we got a numerical solution for the problem of the parachute, so if you have an initial time and velocity for some time t i , you can easily get the velocity at a time t i+1 . This velocity at the time t i+1 can be used to extend the computation to the velocity at t i+2 and so on.
![[object Object],[object Object],f , , Dependent variable Independent variables parameters Forcing functions](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)