Unformatted text preview: c 1 = 0 . 3 and c 2 = 0 . 2. Therefore the equation of motion is given by y ( t ) = 0 . 3 e − 3 t cos 4 t + 0 . 2 e − 3 t sin 4 t (m) . (b) ²rom Problem 32 we know that the frequency of oscillation is given by β/ (2 π ). In part (a) we found that β = 4. Therefore the frequency of oscillation is 4 / (2 π ) = 2 /π . (c) We see a decrease in the frequency of oscillation. We also have the introduction of the factor e − 3 t , which causes the solution to decay to zero. This is a result of energy loss due to the damping. 186...
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 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations, Boundary value problem, initial conditions, e−3t cos, e−3t sin

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