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Consider the general form of the forced spring-mass equation my" +cy' + ky=f(t) (c) Use the...
Consider the following nonhomogeneous linear differential equation ay 6) + by(s) + cy!4) + dy'"' +...
Consider the following nonhomogeneous linear differential equation ay 6) + by(s) + cy!4) + dy'"' + ky'' + my' + ny=3x²3x - 7cos +1 where coefficients a, b, c, d, k, m, n are constant. Assume that the general solution of the associated homogeneous linear differential equation is YAEC,+Ce**+ c xe** + c.xe3* + ecos What is the correct form of the particular solution y of given nonhomogeneous linear differential equation? Yanitiniz: o Yo=Ax*e** + Ex + F **+Cxcos() +oxsin()+Ex+F...
Exercise 3 (6 marks) Consider the forced mass-dampener-spring system that is represented by the differential equa- tion, mx" (t) + ca' (t) + k2(t) = e-t-e-2t where 1. Solve this IVP by usi...
Exercise 3 (6 marks) Consider the forced mass-dampener-spring system that is represented by the differential equa- tion, mx" (t) + ca' (t) + k2(t) = e-t-e-2t where 1. Solve this IVP by using the Method of Undetermined Coefficients (MUC). 2. Solve this IVP by using the Variation of Parameters Method (VOP).
Exercise 3 (6 marks) Consider the forced mass-dampener-spring system that is represented by the differential equa- tion, mx" (t) + ca' (t) + k2(t) = e-t-e-2t where 1. Solve...
(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...
(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()...
Consider the spring-mass system described by the equation my''+By+ky=0, where y denotes the distance from equilibrium....
Consider the spring-mass system described by the equation my''+By+ky=0, where y denotes the distance from equilibrium. Suppose that mass is 3kg and that there is no friction. The spring is stretched by 0.1 m and then struck with a hammer so that y(0)=-0.1 and y'(0)=1, as a result, the mass begins to oscillate at the rate of 4 radians per second. a) What is the spring constant? Justify your answer by computing the homogeneous solution. b) What is the amplitude...
Consider the spring-mass system described by the equation my''+By+ky=0, where y denotes the distance from equilibrium. Suppose that mass is 3kg and that there is no friction. The spring is str...
Consider the spring-mass system described by the equation my''+By+ky=0, where y denotes the distance from equilibrium. Suppose that mass is 3kg and that there is no friction. The spring is stretched by 0.1 m and then struck with a hammer so that y(0)=-0.1 and y'(0)=1, as a result, the mass begins to oscillate at the rate of 4 radians per second. a) What is the spring constant? Justify your answer by computing the homogeneous solution. b) What is the amplitude...
(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...
Problem 13. (1 point) Consider the differential equation y" + ay' + By=t+e3t. Suppose the form...
Problem 13. (1 point) Consider the differential equation y" + ay' + By=t+e3t. Suppose the form of the particular solution to this differential equation as prescribed by the method of undetermined coefficients is yp(t) = Alt + Apt + Bote3t Determine the constants a and B. a= help (numbers) B= help (numbers) Note: You can earn partial credit on this problem.
Consider the nonhomogeneous second order linear equation of the form y" + 2y' + y =...
Consider the nonhomogeneous second order linear equation of the form y" + 2y' + y = g(t). Given that the fundamental solution set of its homogeneous equation is {e**, te' } For each of the parts below, determine the form of particular solution y, that you would use to solve the given equation using the Method of Undetermined Coefficients. DO NOT ATTEMPT TO SOLVE THE COEFFICIENTS. a) y" + 2y' + y = 2te b) y" + 2y' + y...
Consider the following nonhomogeneous linear differential equation ay 6) + by(s) + cy!4) + dy'"' + ky'' + my' + ny=3x²3x - 7cos +1 where coefficients a, b, c, d, k, m, n are constant. Assume that the general solution of the associated homogeneous linear differential equation is YAEC,+Ce**+ c xe** + c.xe3* + ecos What is the correct form of the particular solution y of given nonhomogeneous linear differential equation? Yanitiniz: o Yo=Ax*e** + Ex + F **+Cxcos() +oxsin()+Ex+F...
Exercise 3 (6 marks) Consider the forced mass-dampener-spring system that is represented by the differential equa- tion, mx" (t) + ca' (t) + k2(t) = e-t-e-2t where 1. Solve this IVP by using the Method of Undetermined Coefficients (MUC). 2. Solve this IVP by using the Variation of Parameters Method (VOP).
Exercise 3 (6 marks) Consider the forced mass-dampener-spring system that is represented by the differential equa- tion, mx" (t) + ca' (t) + k2(t) = e-t-e-2t where 1. Solve...
(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...
(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...
Problem 13. (1 point) Consider the differential equation y" + ay' + By=t+e3t. Suppose the form of the particular solution to this differential equation as prescribed by the method of undetermined coefficients is yp(t) = Alt + Apt + Bote3t Determine the constants a and B. a= help (numbers) B= help (numbers) Note: You can earn partial credit on this problem.
Consider the nonhomogeneous second order linear equation of the form y" + 2y' + y = g(t). Given that the fundamental solution set of its homogeneous equation is {e**, te' } For each of the parts below, determine the form of particular solution y, that you would use to solve the given equation using the Method of Undetermined Coefficients. DO NOT ATTEMPT TO SOLVE THE COEFFICIENTS. a) y" + 2y' + y = 2te b) y" + 2y' + y...
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