க Consider the initial value problem my" +cy' +ky = F(t), y(0) = 0, y'(0) = 0 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) = 30 sin(6t) Newtons. a. Solve the initial value problem. y(t)= 887 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. That is, at least some of the terms in the formula go to zero, and those terms are called transient terms. The asymptotic approximating function will not include those transient terms. For very large positive values of t, y(t) ≈0 help (formulas)
க Consider the initial value problem my" +cy' +ky = F(t), y(0) = 0, y'(0) = 0 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) = 30 sin(6t) Newtons. a. Solve the initial value problem. y(t)= 887 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. That is, at least some of the terms in the formula go to zero, and those terms are called transient terms. The asymptotic approximating function will not include those transient terms. For very large positive values of t, y(t) ≈0 help (formulas)
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 = F(t), y(0) = 0, y'(0) = 0
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) = 30 sin(6t) Newtons.
a. Solve the initial value problem.
y(t) =
887
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. That is, at least some of the terms in the formula go to zero, and those terms are called transient terms. The asymptotic
approximating function will not include those transient terms.
For very large positive values of t, y(t) ≈ 0
help (formulas)
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