(1 point) Consider the initial value problem my + cy + ky = F(t), y0 =...
(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, 8 kilograms per second, k = 80 Newtons per meter, and the applied force in Newtons is c if 0tT/2, if t > /2 40 F(t)= a. Solve the initial value...
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 F(t) = 40 sin(6) Newtons. a. Solve the initial value problem. y0) help (formulas) b. Determine the long-term behavior of the system. ls lim y()...
(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(), 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) 60 cos(8t) Newtons. a. Solve the initial value problem. help (formulas) b. Determine the long-term behavior of the system. Is lim y(t)=...
1 point) Consider the initial value problem my "tou' + 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 50 if0 st/2, F(t) = if t > π/2. a Solve the initial value problem, using that the displacement y(t) and...
(1 point) Consider the initial value problem my" + cy' + ky = FO. YO) = 0, y' (O) = 0 modeling the motion of a spring-mass-dashpot system initially at rest and subjected to an applied force FO), where the unit of force is the Newton (N). Assume that m = 2 kilograms, c = 8 kllograms per second, k = 80 Newtons per meter, and F(!) = 30 sin(61) Newtons. a. Solve the initial value problem. M) = help...
Previous Problem ListNext (1 poin) Consider the initial value problestm my" + cy, + k-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 F(t) 20 sin(6t) Newtons a Solve the initial value problem. help (formulas) b. Determine the long-term behavior of the...
Homework7: Problem 24 Problem List Next Problem Previous Problem (1 point) Consider the initial value problem my" +cy'+ky F(t) , (0 ) 0, y 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 klograms, c8 kilograms per second, k 80 Newtons per meter, and the applied force in Newtons is ifosts/2 30 F(0) if t> /2. 0 remain...
Consider the initial value problem y'' + 2y' – 15y = 0, y0) = a, y'0 = 1 Find the value of a so that the solution to the initial value problem approaches zero as t → a= Preview Get help: Video Points possible: 2 Unlimited attempts.
(1 point) A 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 centimeters. At time 0, the resulting mass- spring system is disturbed from its rest state by the force F(t) 70 cos(8t). The force F(t) is expressed in Newtons and is positive in the downward direction, and time is measured in seconds. a. Determine the spring constant k Newtons/meter b. Formulate the initial value problem for y(), where y(t) is the displacement...
having trouble finding y(t) NOT Correct (1 point) Consider the initial value problem y"+16y 48t, y(0)3, /(0)-9. a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y(t) by Y(s). Do not move any terms from one side of the equation to the other (until you get to part (b) below). (s 2Y(s)-3s-9)+16Y(s) help (formulas) 48/s 2 b. Solve your equation for Y(s). C{y(t))=48/(s 2(s2+ 16)...