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Consider the initial value problem y"+yy'+y=k&(t-1), y(0)=0, y'(O)=0, where k is the magnitude of an impulse at t=1 and y is the damping coefficient (or resistance). (a) Let y=1/4. Find the value of k for which the response has a peak value of 6; call this value k1.

Consider the initial value problem y"+yy'+y=k&(t-1), y(0)=0, y'(O)=0, where k is the magnitude of an impulse at t=1 and y is the damping coefficient (or resistance). (a) Let y=1/4. Find the value of k for which the response has a peak value of 6; call this value k1.

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 initial value problem y"+yy'+y=k8(t-1), y(0)=0, y'(0)=0, where k is the magnitude of an impulse at t=1 and y is the damping coefficient (or resistance). (a) Let y=1/4. Find the value of k for which the response has a peak value of 6; call this value k1. Round your answer to two decimal places. k1= (c) Determine how k1 varies as y decreases. What is the value of k1 when y=0 ? k1 as y decreases. k1=
Transcribed Image Text:Consider the initial value problem y"+yy'+y=k8(t-1), y(0)=0, y'(0)=0, where k is the magnitude of an impulse at t=1 and y is the damping coefficient (or resistance). (a) Let y=1/4. Find the value of k for which the response has a peak value of 6; call this value k1. Round your answer to two decimal places. k1= (c) Determine how k1 varies as y decreases. What is the value of k1 when y=0 ? k1 as y decreases. k1=
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