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Consider the initial value problem 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) = my" + cy' + ky = F(t), y(0) = 0, y'(0) = 0 For very large positive values of t, y(t) ~ b. Determine the long-term behavior of the system. Is lim y(t) = 0? If it is, enter zero. If not, enter a function that approximates y(t) for very large positive values of t. 0047 help (formulas) help (formulas)

Consider the initial value problem 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) = my" + cy' + ky = F(t), y(0) = 0, y'(0) = 0 For very large positive values of t, y(t) ~ b. Determine the long-term behavior of the system. Is lim y(t) = 0? If it is, enter zero. If not, enter a function that approximates y(t) for very large positive values of t. 0047 help (formulas) help (formulas)

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter7: Triangles
Section7.5: Vectors: An Algebraic Approach Learning
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Consider the initial value problem 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) = = my" + cy' + ky = F(t), y(0) = 0, y'(0) = 0 For very large positive values of t, y(t) ≈ 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 function that approximates y(t) for very large positive values of t. t→∞ help (formulas)
Transcribed Image Text:Consider the initial value problem 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) = = my" + cy' + ky = F(t), y(0) = 0, y'(0) = 0 For very large positive values of t, y(t) ≈ 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 function that approximates y(t) for very large positive values of t. t→∞ help (formulas)
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