527revexam1

527revexam1 - 642:527 REVIEW EXAM 1 FALL 2009 (16) 1. (a)...

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Unformatted text preview: 642:527 REVIEW EXAM 1 FALL 2009 (16) 1. (a) Find the Laplace transform Y ( s ) of the solution y ( t ) of the initial value problem y + 2 y + 5 y = C ( t- ) , y (0) = 0 , y (0) =- 3 , where C is a constant. (b) Find y ( t ) by taking the inverse Laplace transform of Y ( s ). (c) Find a value for C such that y ( t ) is constant for t > . What is this constant value? (d) Suppose that this equation describes the motion of a a mass hanging from a support, to which it is connected by a spring. Physically speaking, what does the delta function represent? Why does the mass stop moving? (12) 2. A function f ( t ) is defined for t 0 by f ( t ) = braceleftbigg ( t- 2) 2 , if 2 t < 3, , if 0 t < 2 or t 3. Express f ( t ) in terms of a single formula using the Heaviside function, then find its Laplace transform. (10) 3. Find the inverse Laplace transform of Y ( s ) = 2 s + 5 s 3 + s 2- 2 s ....
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527revexam1 - 642:527 REVIEW EXAM 1 FALL 2009 (16) 1. (a)...

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