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 c = 8 kilograms per second, k = 80 Newtons per meter, and F(t) = 80 cos(8t) Newtons. 2 kilograms,
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 c = 8 kilograms per second, k = 80 Newtons per meter, and F(t) = 80 cos(8t) Newtons. 2 kilograms,
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Transcribed Image Text:тa" + сa' + kх —D
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,
c = 8 kilograms per second, k = 80 Newtons per meter, and F(t) = 80 cos(8t) Newtons.
Solve the initial value problem.
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,
æ(t) z xsp(t)
help
(formulas)
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