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Consider the initial value problem my" + cy' + ky = F(t), y(0) = 0, y'(0) = 0

Consider the initial value problem my" + cy' + ky = F(t), y(0) = 0, y'(0) = 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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Consider the initial value problem my" + cy' + ky: = modeling the motion of a spring-mass-dashpot system initially at rest and subjected to an applied force F(t), where the unit of force is the Newton (N). Assume that m = 2 kilograms, c = 8 kilograms per second, k = 80 Newtons per meter, and F(t) = 40 sin(6t) Newtons. a. Solve the initial value problem. y(t): = e^(-2t) F(t), y(0) = 0, y'(0) = 0 (30/37cos(6t)+5/37sin(6t))-30/37cos(6t)+5 help (formulas) b. Determine the long-term behavior of the system. Is lim y(t) = 0? If it is, enter zero. If not, enter a t→∞ function that approximates y(t) for very large positive values of t. For very large positive values of t, y(t) ≈ 0 help (formulas)
Transcribed Image Text:Consider the initial value problem my" + cy' + ky: = modeling the motion of a spring-mass-dashpot system initially at rest and subjected to an applied force F(t), where the unit of force is the Newton (N). Assume that m = 2 kilograms, c = 8 kilograms per second, k = 80 Newtons per meter, and F(t) = 40 sin(6t) Newtons. a. Solve the initial value problem. y(t): = e^(-2t) F(t), y(0) = 0, y'(0) = 0 (30/37cos(6t)+5/37sin(6t))-30/37cos(6t)+5 help (formulas) b. Determine the long-term behavior of the system. Is lim y(t) = 0? If it is, enter zero. If not, enter a t→∞ function that approximates y(t) for very large positive values of t. For very large positive values of t, y(t) ≈ 0 help (formulas)
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