1 Point Consider The Initial Value Problem My Cy Ky F T Y 0 0 Y 0 0 Modeling The Motion Of A Spring 1 (55.32 KiB) Viewed 39 times
1 Point Consider The Initial Value Problem My Cy Ky F T Y 0 0 Y 0 0 Modeling The Motion Of A Spring 2 (38.16 KiB) Viewed 39 times
1 Point Consider The Initial Value Problem My Cy Ky F T Y 0 0 Y 0 0 Modeling The Motion Of A Spring 3 (28.73 KiB) Viewed 39 times
(1 point) 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 = 2 kilograms, c = 8 kilograms per second, k = 80 Newtons per meter, and the applied force in Newtons is F(t) = { 40 0 if 0 ≤ t ≤ л/2, if t > π/2. a. Solve the initial value problem, using that the displacement y(t) and velocity y' (t)
a. Solve the initial value problem, using that the displacement y(t) and velocity y' (t) remain continuous when the applied force is discontinuous. For 0 ≤ t ≤ л/2, y(t) = help (formulas) For tл/2, y(t) = help (formulas) b. Determine the long-term behavior of the evetom le lim y(t) = 02 If it is antar -
b. Determine the long-term behavior of the system. Is lim y(t) = 0? If it is, enter 1→∞ 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) ~ help (formulas)
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