527revexam1

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

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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 = Cδ ( t- π ) , 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 > π . 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 Find...

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