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9. Consider the forced spring-mass system governed by the equation y" + 2y + 2y = 2 cos(t) (a) What is the mass of the object, the damping coefficient, the spring constant and the external force for this system? (b) Find the general solution to the differential equation. Identify the fundamental set for solutions to the corresponding homogeneous equation and the particular solution to the nonhomogeneous equation that appears in your general solution. (c) Solve the IVP with initial conditions y(0) = 2 and y'(0) = 0. (d) Find a different fundamental set for solutions to the homogeneous equation and a different particular solution to the nonhomogeneous equation.

9. Consider the forced spring-mass system governed by the equation y" + 2y + 2y = 2 cos(t) (a) What is the mass of the object, the damping coefficient, the spring constant and the external force for this system? (b) Find the general solution to the differential equation. Identify the fundamental set for solutions to the corresponding homogeneous equation and the particular solution to the nonhomogeneous equation that appears in your general solution. (c) Solve the IVP with initial conditions y(0) = 2 and y'(0) = 0. (d) Find a different fundamental set for solutions to the homogeneous equation and a different particular solution to the nonhomogeneous equation.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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9. a. The mass of the object m = 1, the damping constant y = 2, the spring constant k = 2, and the external force is F(t) = 2 cos(t). b. y = e-t(c₁ cost + c₂ sin t) + ² cos t + sin t 5 et (c₁ cost + C₂ sin t) Fundamental set of solutions to the corresponding homogeneous equation: {e-t cost, et sin t} Particular solution to nonhomogeneous equation: yp = costsin t Yn = (co cost + sint) + cost + sint c. y = e-t d. Fundamental set of solutions to the corresponding homogeneous equation (for example): {e-t cost + et sint, et cost- e-t sin t} (verify both are solutions and are LI; the Wronskian W = -2e-²t # 0) Particular solution to nonhomogeneous equation (for example): y = et cost + cost + sin t 5 5
Transcribed Image Text:9. a. The mass of the object m = 1, the damping constant y = 2, the spring constant k = 2, and the external force is F(t) = 2 cos(t). b. y = e-t(c₁ cost + c₂ sin t) + ² cos t + sin t 5 et (c₁ cost + C₂ sin t) Fundamental set of solutions to the corresponding homogeneous equation: {e-t cost, et sin t} Particular solution to nonhomogeneous equation: yp = costsin t Yn = (co cost + sint) + cost + sint c. y = e-t d. Fundamental set of solutions to the corresponding homogeneous equation (for example): {e-t cost + et sint, et cost- e-t sin t} (verify both are solutions and are LI; the Wronskian W = -2e-²t # 0) Particular solution to nonhomogeneous equation (for example): y = et cost + cost + sin t 5 5
9. Consider the forced spring-mass system governed by the equation y" + 2y' + 2y = 2 cos(t) (a) What is the mass of the object, the damping coefficient, the spring constant and the external force for this system? (b) Find the general solution to the differential equation. Identify the fundamental set for solutions to the corresponding homogeneous equation and the particular solution to the nonhomogeneous equation that appears in your general solution. (c) Solve the IVP with initial conditions y(0) = 2 and y'(0) = 0. (d) Find a different fundamental set for solutions to the homogeneous equation and a different particular solution to the nonhomogeneous equation.
Transcribed Image Text:9. Consider the forced spring-mass system governed by the equation y" + 2y' + 2y = 2 cos(t) (a) What is the mass of the object, the damping coefficient, the spring constant and the external force for this system? (b) Find the general solution to the differential equation. Identify the fundamental set for solutions to the corresponding homogeneous equation and the particular solution to the nonhomogeneous equation that appears in your general solution. (c) Solve the IVP with initial conditions y(0) = 2 and y'(0) = 0. (d) Find a different fundamental set for solutions to the homogeneous equation and a different particular solution to the nonhomogeneous equation.
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