Question

Consider the initial 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 = 8 kilograms, k = 80 Newtons per meter, and F(t) = 100 cos(8t) Newtons. a. Solve the initial value problem: y(t) = b. Determine the long-term behavior of the system: Is lim y(t) = 0? If it is, enter zero. If not, enter a function that approximates y(t) for very large positive values of t. For very large positive values of t, y(t) =

          Consider the initial 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 = 8 kilograms, k = 80 Newtons per meter, and F(t) = 100 cos(8t) Newtons.

a. Solve the initial value problem:
y(t) = 

b. Determine the long-term behavior of the system: Is lim y(t) = 0? If it is, enter zero. If not, enter a function that approximates y(t) for very large positive values of t.
For very large positive values of t, y(t) =

point consider the initial value problem my cy ky ft y0 0 y 0 0 modeling the motion of spring mass dashpot system initially at rest and subjected to an applied force ft where the unit of for 22012

Added by Jordi V.

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