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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
please solve it on paper ( you can see the answers in the other pic)
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
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.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
