my" + cy' + ky = F(t), y(0) = 0, y'(0) - 0 modeling the motion of a spring-mass-dashpot system initialy 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 the applied force in Newtons is 20 if 0/2. a Solve the initial value problem, using that the displacement y(t) and velocity y'(1) remain continuous when the applied force is discontinuous For 0sts/2 pl(t) = help (formulas) For t> /2. y(t) = help (formutas) D. Determine the long-term behavior of the system is lim y(t) = 07 Iftis, enter zero. If not, enter a function that approximates y(t) for E-100 very large positive values of t. For very large positive values of t y(t) help (formulas)
my" + cy' + ky = F(t), y(0) = 0, y'(0) - 0 modeling the motion of a spring-mass-dashpot system initialy 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 the applied force in Newtons is 20 if 0/2. a Solve the initial value problem, using that the displacement y(t) and velocity y'(1) remain continuous when the applied force is discontinuous For 0sts/2 pl(t) = help (formulas) For t> /2. y(t) = help (formutas) D. Determine the long-term behavior of the system is lim y(t) = 07 Iftis, enter zero. If not, enter a function that approximates y(t) for E-100 very large positive values of t. For very large positive values of t y(t) 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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Transcribed Image Text:Consider the inital value problem
my" + cy' + ky = F(t), y(0) = 0, y'(0) = 0
!!
modeling the motion of a spring-mass-dashpot 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 the applied force in Newtons is
S20
if 0<tSx/2,
F(t) =
10
if t> */2.
a Solve the initial value problem, using that the displacement y(t) and velocity y'(1) remain continuous when the applied force is
discontinuous
For 0stS/2. v(t) =
help (formulas)
For t> =/2. v(t) =
help (formulas)
b. Determine the long-term behavior of the system. Is lim y(t) = 07 If it is, enter zero. If not, enter a function that approximates y(t) for
t-00
very large positive values of t
For very large positive values of t, y(t)
help (formulas)
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