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8) A system with a 20X + (1000 + 23 * 31)x = F(t) differential equation is subjected to a force as shown below. Obtain the displacement of the mass for the two modes 0 ≤ t ≤ 40 and t≥ 40 by the following two methods. A) For using the convolution integral (just write the integrals with a certain range and explain the method. There is no need to calculate the integrals) B) Using the superposition method

8) A system with a 20X + (1000 + 23 * 31)x = F(t) differential equation is subjected to a force as shown below. Obtain the displacement of the mass for the two modes 0 ≤ t ≤ 40 and t≥ 40 by the following two methods. A) For using the convolution integral (just write the integrals with a certain range and explain the method. There is no need to calculate the integrals) B) Using the superposition method

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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8) A system with a 20X + (1000 + 23 * 31)x = F(t) differential equation is subjected to a force as shown below. Obtain the displacement of the mass for the two modes 0 ≤ t ≤ 40 and t≥ 40 by the following two methods. A) For using the convolution integral (just write the integrals with a certain range and explain the method. There is no need to calculate the integrals) B) Using the superposition method Step answer x(t) = (1 - cos w₁t) Slope response (t): (@nt - sin wnt) SF wnk mware-Cun(t-r) sinwa(t - 7)dr x(t): = SF A+500 F(t), N A+300 0 0 40 t, sec
Transcribed Image Text:8) A system with a 20X + (1000 + 23 * 31)x = F(t) differential equation is subjected to a force as shown below. Obtain the displacement of the mass for the two modes 0 ≤ t ≤ 40 and t≥ 40 by the following two methods. A) For using the convolution integral (just write the integrals with a certain range and explain the method. There is no need to calculate the integrals) B) Using the superposition method Step answer x(t) = (1 - cos w₁t) Slope response (t): (@nt - sin wnt) SF wnk mware-Cun(t-r) sinwa(t - 7)dr x(t): = SF A+500 F(t), N A+300 0 0 40 t, sec
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