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Consider the following initial value problem, representing the response of an undamped oscillator subject to the ramp loading applied force g(t): 0. 0

Consider the following initial value problem, representing the response of an undamped oscillator subject to the ramp loading applied force g(t): 0. 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I got stuck after finding the first term of G(t). 

Consider the following initial value problem, representing the response of an undamped oscillator subject to the ramp loading applied force g(t): 0. 0<t< 4, 4 4 <t< 8, t " + 16у — 9(t), у(0) — 0, /(0) — — 2, 9(t) — y(0) = -2, g(t) = 4 1 otherwise. In the following parts, use h(t - c) for the Heaviside function h(t) when necessary. | a. First, compute the Laplace transform of g(t). L {f(t)}(s) = b. Next, take the Laplace transform of the left-hand-side of the differential equation, set it equal to your answer from Part a. and solve for L {y(t)}. L {y(t)}(s) = c. Lastly, take the inverse Laplace transform to compute y(t). y(t) =
Transcribed Image Text:Consider the following initial value problem, representing the response of an undamped oscillator subject to the ramp loading applied force g(t): 0. 0<t< 4, 4 4 <t< 8, t " + 16у — 9(t), у(0) — 0, /(0) — — 2, 9(t) — y(0) = -2, g(t) = 4 1 otherwise. In the following parts, use h(t - c) for the Heaviside function h(t) when necessary. | a. First, compute the Laplace transform of g(t). L {f(t)}(s) = b. Next, take the Laplace transform of the left-hand-side of the differential equation, set it equal to your answer from Part a. and solve for L {y(t)}. L {y(t)}(s) = c. Lastly, take the inverse Laplace transform to compute y(t). y(t) =
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