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Unformatted text preview: COT 3502 Computer Model Formulation Spring 2008 1 Homework # 8 Due Tuesday, April 15 Problems 1-2 are theoretical. Problems 3-5 should be solved using VB. 1. (3 points) Consider the system of ordinary differential equations d x dt = A x , A = 2- 1 1 ! . (1) (a) Obtain the eigenvalue, the eigenvector, and the generalized eigenvec- tor of the matrix A . (b) Obtain a general solution of this system of equations. (c) Obtain solution satisfying initial conditions x (0) = (2 , 1). 2. (3 points) In class, we considered an equation for oscillations of a mass attached to a spring assuming that the friction force is negligible. (a) Modify the equation derived in class and obtain an ODE that de- scribes the oscillations in the case of a non-negligible friction. As- sume that the friction force is given by F =- γv , where γ is the friction coefficient and v is the velocity. (b) Obtain a general real solution of this equation assuming that the mass is m = 1 kg, the spring constant is k = 4 N/m, and the friction...
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- Spring '08
- Friction Force, Midpoint method, ﬁrst order odes