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Consider the initial value problem mx" cx' + kx F(t), x(0) = 0, x'(0) = 0 modeling the motion of a damped mass-spring 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 80 Newtons per meter, and F(t) = 20 sin(6t) kilograms, c = 8 kilograms per second, k = Newtons. Solve the initial value problem. x(t) = help (formulas) Determine the long-term behavior of the system (steady periodic solution). Is lim x(t) = 0 0047 ? If it is, enter zero. If not, enter a function that approximates x(t) for very large positive values of t. For very large positive values of t, x(t) ≈ x sp(t) = ☐ help (formulas) Book: Section 2.6 of Notes on Diffy Qs

Consider the initial value problem mx" cx' + kx F(t), x(0) = 0, x'(0) = 0 modeling the motion of a damped mass-spring 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 80 Newtons per meter, and F(t) = 20 sin(6t) kilograms, c = 8 kilograms per second, k = Newtons. Solve the initial value problem. x(t) = help (formulas) Determine the long-term behavior of the system (steady periodic solution). Is lim x(t) = 0 0047 ? If it is, enter zero. If not, enter a function that approximates x(t) for very large positive values of t. For very large positive values of t, x(t) ≈ x sp(t) = ☐ help (formulas) Book: Section 2.6 of Notes on Diffy Qs

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 18EQ
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Consider the initial value problem mx" cx' + kx F(t), x(0) = 0, x'(0) = 0 modeling the motion of a damped mass-spring 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 80 Newtons per meter, and F(t) = 20 sin(6t) kilograms, c = 8 kilograms per second, k = Newtons. Solve the initial value problem. x(t) = help (formulas) Determine the long-term behavior of the system (steady periodic solution). Is lim x(t) = 0 0047 ? If it is, enter zero. If not, enter a function that approximates x(t) for very large positive values of t. For very large positive values of t, x(t) ≈ x sp(t) = ☐ help (formulas) Book: Section 2.6 of Notes on Diffy Qs
Transcribed Image Text:Consider the initial value problem mx" cx' + kx F(t), x(0) = 0, x'(0) = 0 modeling the motion of a damped mass-spring 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 80 Newtons per meter, and F(t) = 20 sin(6t) kilograms, c = 8 kilograms per second, k = Newtons. Solve the initial value problem. x(t) = help (formulas) Determine the long-term behavior of the system (steady periodic solution). Is lim x(t) = 0 0047 ? If it is, enter zero. If not, enter a function that approximates x(t) for very large positive values of t. For very large positive values of t, x(t) ≈ x sp(t) = ☐ help (formulas) Book: Section 2.6 of Notes on Diffy Qs
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