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Unformatted text preview: is the spring constant, b the (constant) damping coecient, v = x t the velocity and a = v t = x tt the acceleration. 1. Show that this 2nd order ODE is equivalent to the 1st order linear system of ODEs x v t = 1-k m-b m x v 2. Assume that we are using Forward Euler to solve this system numerically, with a timestep equal to t . If 1 , 2 C are the complex eigenvalues of the matrix 1 t-k t m 1-b t m show that the condition for stability is k 1 k < 1 and k 2 k < 1 3. Show that if b 2 < 4 km (such spring systems are referred to as under-damped ), then the eigenvalues of the matrix above are given as 1 , 2 = 1-b t 2 m i t 2 m p 4 km-b 2 4. Show that if b 2 < 4 km the condition for stability is t < b/k . 2...
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This homework help was uploaded on 01/29/2008 for the course CS 205A taught by Professor Fedkiw during the Fall '07 term at Stanford.
- Fall '07