(D) In the following LTIODES, find all values of K that produce a stable homogeneous solution with settling time less than 2 seconds. Use function roots (or your calculator) to illustrate one value of K that works, and one that doesn't. In other words, choose a specific numerical value of K which produces a settling time less than 2 seconds, and calculate the actual roots for that K; then choose a specific numerical value for K which produces a settling time slower than 2 seconds, and calculate the actual roots for that K 1. 2. 3. 4. x(t)+9x(t) +28x(t) + Kx(t) = 0 x(t) +7x(t) + Kx(t) +24x(t) = 0 x(t)+8x(t) + 40(t) + 96x(t) + Kx(t) = 0 x(t) +8x(t) + Kä(t) +96x(t) + 80x(t) = 0
(D) In the following LTIODES, find all values of K that produce a stable homogeneous solution with settling time less than 2 seconds. Use function roots (or your calculator) to illustrate one value of K that works, and one that doesn't. In other words, choose a specific numerical value of K which produces a settling time less than 2 seconds, and calculate the actual roots for that K; then choose a specific numerical value for K which produces a settling time slower than 2 seconds, and calculate the actual roots for that K 1. 2. 3. 4. x(t)+9x(t) +28x(t) + Kx(t) = 0 x(t) +7x(t) + Kx(t) +24x(t) = 0 x(t)+8x(t) + 40(t) + 96x(t) + Kx(t) = 0 x(t) +8x(t) + Kä(t) +96x(t) + 80x(t) = 0
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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Transcribed Image Text:(D) In the following LTIODES, find all values of K that produce a stable homogeneous solution with settling time
less than 2 seconds. Use function roots (or your calculator) to illustrate one value of K that works, and one that
doesn't. In other words, choose a specific numerical value of K which produces a settling time less than 2 seconds,
and calculate the actual roots for that K; then choose a specific numerical value for K which produces a settling
time slower than 2 seconds, and calculate the actual roots for that K
1.
2.
3.
4.
x(t)+9x(t) +28x(t) + Kx(t) = 0
x(t) +7x(t) + Kx(t) +24x(t) = 0
x(t)+8x(t) + 40(t) + 96x(t) + Kx(t) = 0
x(t) +8x(t) + Kä(t) +96x(t) + 80x(t) = 0
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