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Unformatted text preview: 1. Find the general solution to the following systems of equations and for (a) sketch the phase space diagram: (a) x = ˙ 3 −2 2 −2 x, (b) x = ˙ 3 −2 4 −1 x. 2. Solve the following initial value problem: x= ˙ 5 −1 3 1 x, x(0) = 2 −1 . 3. Consider x= ˙ 0 1 −5 α x. (a) Determine the eigenvalues in terms of α. (b) Determine the values of α for which the origin is an attractant or repellant. Also, for which values of α is the origin a node, an improper node, a saddle point or a spiral point. 4. By a normal mode analysis, ﬁnd the general solution for two masses of mass m1 and m2 connected by a spring with spring constant k . 1 ...
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This note was uploaded on 01/28/2011 for the course MATH 150 taught by Professor T.qian during the Spring '09 term at HKUST.
 Spring '09
 T.Qian
 Systems Of Equations, Equations

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