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(1 point) Consider the initial value problem my" + cy' + ky = FO. YO) =...
(1 point) Consider the initial value problem my"+cy'+ky F(t), y(0) = 0, y'(0) = 0 modeling...
(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" +cy' + ky-F(t), y' (0)-0 y(0)-0, modeling the...
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...
(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), y0 =...
(1 point) Consider the initial value problem my + cy + ky = F(t), y0 = 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 (20 if 0 <t< /2, F(t) = 30...
Previous Problem ListNext (1 poin) Consider the initial value problestm my" + cy, + k-F(t), y(0)-0,...
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...
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...
1 point) Consider the initial value problem my "tou' + ky-F(t), y(0)-0, y"(0)-0 modeling the motion...
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) A 10 kilogram object suspended from the end of a vertically hanging spring stretches th...
(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...
Consider the initial value problem dy 3 2- y = 3t + 2e', y(0) = yo...
Consider the initial value problem dy 3 2- y = 3t + 2e', y(0) = yo . and for yo > Ye, (a) Find the critical value of yo, yc, such that for yo < yc, limt 400 y(t) = - limt700 y(t) = 0. (b) What happens if yo = ye?
please help with entire question 7(0) = -5. Consider the initial value problem 47" + 28y'...
please help with entire question
7(0) = -5. Consider the initial value problem 47" + 28y' +49-0, (0) - 1, (a) Solve the initial value problem. X(t) Plot its solution for osts 5. (A computer algebra system is recommended.) (b) Determine where the solution has the value zero. (c) Determine the coordinates (to, Yo) of the minimum point. (to yo)-( (d) Change the second initial condition to y(0) -b and find the solution as a function of b. Xt) Find...
(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" +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(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), y0 = 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 (20 if 0 <t< /2, F(t) = 30...
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...
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) 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...
Consider the initial value problem dy 3 2- y = 3t + 2e', y(0) = yo . and for yo > Ye, (a) Find the critical value of yo, yc, such that for yo < yc, limt 400 y(t) = - limt700 y(t) = 0. (b) What happens if yo = ye?
please help with entire question
7(0) = -5. Consider the initial value problem 47" + 28y' +49-0, (0) - 1, (a) Solve the initial value problem. X(t) Plot its solution for osts 5. (A computer algebra system is recommended.) (b) Determine where the solution has the value zero. (c) Determine the coordinates (to, Yo) of the minimum point. (to yo)-( (d) Change the second initial condition to y(0) -b and find the solution as a function of b. Xt) Find...
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