Consider the initial value problem ma" + cx' + kr = F(t), 2(0) = 0, '(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, e = 8 kilograms per second, k=80 Newtons per meter, and F(t) = 50e Newtons. Solve the initial value problem. z(t) = help (formulas) Determine the long-term behavior of the system (steady periodic solution). Is lim z(t) = 0? If it is, enter zero. If not, enter a function that approximates a(t) for very large positive values of t. t-00 For very large positive values of t. (t) Top(t) 0 P help (formulas)
Consider the initial value problem ma" + cx' + kr = F(t), 2(0) = 0, '(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, e = 8 kilograms per second, k=80 Newtons per meter, and F(t) = 50e Newtons. Solve the initial value problem. z(t) = help (formulas) Determine the long-term behavior of the system (steady periodic solution). Is lim z(t) = 0? If it is, enter zero. If not, enter a function that approximates a(t) for very large positive values of t. t-00 For very large positive values of t. (t) Top(t) 0 P 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
ma" + cx + kr = F(t), 2(0) = 0, '(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, e = 8 kilograms per
second, k=80 Newtons per meter, and F(t) = 50e Newtons.
Solve the initial value problem.
z(t)=
help (formulas)
Determine the long-term behavior of the system (steady periodic solution). Is lim z(t) = 0? If it is, enter
zero. If not, enter a function that approximates z(t) for very large positive values of t.
t-00
For very large positive values of t.
(t) Top(t) 0
Submit answer
help (formulas)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbf7838de-33b1-4c9b-b444-de4b7c84d20a%2F41ae6aa5-e1ad-4901-bce8-f01d72ee7078%2F1373we_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the initial value problem
ma" + cx + kr = F(t), 2(0) = 0, '(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, e = 8 kilograms per
second, k=80 Newtons per meter, and F(t) = 50e Newtons.
Solve the initial value problem.
z(t)=
help (formulas)
Determine the long-term behavior of the system (steady periodic solution). Is lim z(t) = 0? If it is, enter
zero. If not, enter a function that approximates z(t) for very large positive values of t.
t-00
For very large positive values of t.
(t) Top(t) 0
Submit answer
help (formulas)
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