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e motion of a damped mass-spring system initially at rest

e motion of a damped mass-spring system initially at rest

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 59E: According to the solution in Exercise 58 of the differential equation for Newtons law of cooling,...
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Consider the initial value problem тx" + сx' + 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). 8 kilograms per second, k = 80 Newtons 2 kilograms, c= per meter, and F(t) = 40 sin(6t) Newtons. Assume that m = Solve the initial value problem. e^(-2t)((3/10)cos(6t)-(13/30)sin(6t))-(3cos(8t))/10+ (2sin(18t))/5 æ(t) = 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) = (-3cos(8t))/10+(2sin(8t))/5 help (formulas)
Transcribed Image Text:Consider the initial value problem тx" + сx' + 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). 8 kilograms per second, k = 80 Newtons 2 kilograms, c= per meter, and F(t) = 40 sin(6t) Newtons. Assume that m = Solve the initial value problem. e^(-2t)((3/10)cos(6t)-(13/30)sin(6t))-(3cos(8t))/10+ (2sin(18t))/5 æ(t) = 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) = (-3cos(8t))/10+(2sin(8t))/5 help (formulas)
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Calculus For The Life Sciences
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ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
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