Problem 9. Consider a horizontal mass-spring system with mass 10 kg and spring constant 10 N/m. a. If the surface the mass slides on is frictionless and there are no external forces, setup and solve the model for the position of the spring as a function of time. See the last page of this review for relevant eigenvalues and eigenvectors. b. Suppose the force due to friction is proportional to the velocity of the mass with proportionality constant 20 Ns/m. Setup and solve the new model for the position of the spring as a function of time. See the last page of this review for relevant eigenvalues and eigenvectors. c. Is the mass-spring system calculated in part b underdamped, critically damped, or overdamped? Explain your reasoning.

Problem 9. Consider a horizontal mass-spring system with mass 10 kg and spring constant 10 N/m. a. If the surface the mass slides on is frictionless and there are no external forces, setup and solve the model for the position of the spring as a function of time. See the last page of this review for relevant eigenvalues and eigenvectors. b. Suppose the force due to friction is proportional to the velocity of the mass with proportionality constant 20 Ns/m. Setup and solve the new model for the position of the spring as a function of time. See the last page of this review for relevant eigenvalues and eigenvectors. c. Is the mass-spring system calculated in part b underdamped, critically damped, or overdamped? Explain your reasoning.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

Eigenvalues and Eigenvectors for Problems 9 and 10.
0 1
-i
has eigenvalues i and -i along with corresponding eigenvectors
and
respectively.
(:).
1
has only one eigenvalue of –1 with corresponding eigenspace spanned by the single
-1
-2
-1
eigenvector
-1- 2i
1
has eigenvalues –1+2i and –1-2i along with corresponding eigenvectors
-5
-2
-1+ 2i
and
respectively.
5

Problem 9. Consider a horizontal mass-spring system with mass 10 kg and spring constant 10 N/m.
a. If the surface the mass slides on is frictionless and there are no external forces, setup and solve the
model for the position of the spring as a function of time. See the last page of this review for relevant
eigenvalues and eigenvectors.
b. Suppose the force due to friction is proportional to the velocity of the mass with proportionality constant
20 Ns/m. Setup and solve the new model for the position of the spring as a function of time. See the
last page of this review for relevant eigenvalues and eigenvectors.
c. Is the mass-spring system calculated in part b underdamped, critically damped, or overdamped? Explain
your reasoning.
d. Suppose that the proportionality constant in part b is 15 Ns/m instead. Would the new system be
underdamped, critically damped, or overdamped? Explain your reasoning.

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