MATH 4B Lecture Notes - Lecture 7: Xist (Gene), Feasible Region, Coset
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Lecture 07 a classi cation of solutions to homogenous second order linear differential equations with constant coef cient y. 45-0 di and as distinct eigenvalues y-e. eittcse. tt x. is a repeated eigenvalues y-e. etttcste. at. Xist of i. bed - fi y=gedtcosfttczedtsinft . How to compute the solutions toy "t2y" solution : y-kehtitttk. eu. it. = e-tcwst-is. int) ysqe-twst-c. e-ts. int tzy-ox-bt. tl#bx=-2ifzi=-2tzi-4=-ztzi finish damped oscillation . e. g . ay"tby"tcy=o and x=3i4i. A classical application of complex eigenvalues is that of spring problem . upspring. If a spring is pulled e compressed) x them neutral length then this exerts a force proportional to x. " "t kx = o tats string constant . Given a mass of 2kg , an spring of. It we require a force of 64n to stretch it to a length of t. fm then hooke"s law says : These types of oscillating systems are generally . interacted with periodically. Mx tx "t kx = fo co sunt thx t jx "t kx.
