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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

Consider the following initial value problem, representing the response of an undamped oscillator subject to the ramp loading applied force g(t): 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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Consider the following initial value problem, representing the response of an undamped oscillator subject to loading applied force g(t): the ramp 0 <t < 3, t - 3 y" + 16y = g(t), y(0) = 0, y/(0) = -3, g(t) = 3 <t < 6, 3 1 otherwise. In the following parts, use h(t – c) for the Heaviside function he(t) when necessary. a. First, compute the Laplace transform of g(t). -3s -6s te L{f(t)}(s) = 382 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)}. -3s -6s e e L{y(t)}(s) = 352(,? + 16)
Transcribed Image Text:Consider the following initial value problem, representing the response of an undamped oscillator subject to loading applied force g(t): the ramp 0 <t < 3, t - 3 y" + 16y = g(t), y(0) = 0, y/(0) = -3, g(t) = 3 <t < 6, 3 1 otherwise. In the following parts, use h(t – c) for the Heaviside function he(t) when necessary. a. First, compute the Laplace transform of g(t). -3s -6s te L{f(t)}(s) = 382 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)}. -3s -6s e e L{y(t)}(s) = 352(,? + 16)
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