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Solve y" + y = F(t), in which F(t) = 1– t²/n² if 0

Solve y" + y = F(t), in which F(t) = 1– t²/n² if 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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Solve y" + y = F (t), in which F(t) = 1 – t? /n² if 0 <t<n and F(t) = 0 if n< t; here, y(0) = 0, y'(0) = 0. This models an undamped system on which a force acts during some interval of time, for instance, the force on a gun barrel when a shell is fired, the barrel being braked by heavy springs (and then damped by a dashpot, which we disregard for simplicity). Hint: At a both y and y' must be continuous. t
Transcribed Image Text:Solve y" + y = F (t), in which F(t) = 1 – t? /n² if 0 <t<n and F(t) = 0 if n< t; here, y(0) = 0, y'(0) = 0. This models an undamped system on which a force acts during some interval of time, for instance, the force on a gun barrel when a shell is fired, the barrel being braked by heavy springs (and then damped by a dashpot, which we disregard for simplicity). Hint: At a both y and y' must be continuous. t
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