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You have been provided with the following innitial value problem: Y"+16y= g(t), y(0)= 0, y'(0)=0 (1) = e Where g(t)= 't if 0 ≤ t <5 if 5≤ t ≤00

You have been provided with the following innitial value problem: Y"+16y= g(t), y(0)= 0, y'(0)=0 (1) = e Where g(t)= 't if 0 ≤ t <5 if 5≤ t ≤00

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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You have been provided with the following innitial value problem: Y"+16y= g(t), y(o)= 0, y'(0)=0 Where g(t)= ={t 't if 0 ≤ t <5 if 5≤ t ≤00 Apply the Laplace transform to both sides of the provided differential equation in order to derive the corresponding algebraic equation. Represent the Laplace transform of the function y(t) as Y(s). Avoid transferring terms between different sides of the equation until reaching part (b) as described below. Now solve the equation you found for Y(s): Y(s)=L{y(t)}= y(t)= Perform the inverse Laplace transform on both sides of the equation from the preceding step to find the solution for the function y(t).if need be, utilize h(t) to symbolize the Heaviside function: 0 if t ≤0 h(t)= If ost
Transcribed Image Text:You have been provided with the following innitial value problem: Y"+16y= g(t), y(o)= 0, y'(0)=0 Where g(t)= ={t 't if 0 ≤ t <5 if 5≤ t ≤00 Apply the Laplace transform to both sides of the provided differential equation in order to derive the corresponding algebraic equation. Represent the Laplace transform of the function y(t) as Y(s). Avoid transferring terms between different sides of the equation until reaching part (b) as described below. Now solve the equation you found for Y(s): Y(s)=L{y(t)}= y(t)= Perform the inverse Laplace transform on both sides of the equation from the preceding step to find the solution for the function y(t).if need be, utilize h(t) to symbolize the Heaviside function: 0 if t ≤0 h(t)= If ost
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