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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 kilograms, 8 kilograms per second, k 80 Newtons per meter, and F(t) = 100 cos(8t) Newtons. C = Solve the initial value problem. x(t) e^(-2t)(0.75cos(6t)-1.08333sin(6t))+15/100(4sin(8t)-3cos(8t)) help (formulas) Determine the long-term behavior of the system (steady periodic solution). Is lim x(t) = 0? 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) 2 xsp (t) = help

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 kilograms, 8 kilograms per second, k 80 Newtons per meter, and F(t) = 100 cos(8t) Newtons. C = Solve the initial value problem. x(t) e^(-2t)(0.75cos(6t)-1.08333sin(6t))+15/100(4sin(8t)-3cos(8t)) help (formulas) Determine the long-term behavior of the system (steady periodic solution). Is lim x(t) = 0? 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) 2 xsp (t) = help

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 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 kilograms, 8 kilograms per second, k 80 Newtons per meter, and F(t) = 100 cos(8t) Newtons. C = Solve the initial value problem. x(t) e^(-2t)(0.75cos(6t)-1.08333sin(6t))+15/100(4sin(8t)-3cos(8t)) help (formulas) Determine the long-term behavior of the system (steady periodic solution). Is lim x(t) = 0? 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) 2 xsp (t) = help
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 kilograms, 8 kilograms per second, k 80 Newtons per meter, and F(t) = 100 cos(8t) Newtons. C = Solve the initial value problem. x(t) e^(-2t)(0.75cos(6t)-1.08333sin(6t))+15/100(4sin(8t)-3cos(8t)) help (formulas) Determine the long-term behavior of the system (steady periodic solution). Is lim x(t) = 0? 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) 2 xsp (t) = help
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