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Problem 10. Consider a horizontal mass-spring system with mass 10 kg, spring constant 50 N/m, and force due to friction proportional to the velocity of the mass with proportionality constant 20 Ns/m. a. 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.

Problem 10. Consider a horizontal mass-spring system with mass 10 kg, spring constant 50 N/m, and force due to friction proportional to the velocity of the mass with proportionality constant 20 Ns/m. a. 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.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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Problem 10. Consider a horizontal mass-spring system with mass 10 kg, spring constant 50 N/m, and force due to friction proportional to the velocity of the mass with proportionality constant 20 Ns/m. a. 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 an external force of F(t) = 10 sin t is applied to the mass-spring system. Setup and solve the new model for the position of the spring as a function of time.
Transcribed Image Text:Problem 10. Consider a horizontal mass-spring system with mass 10 kg, spring constant 50 N/m, and force due to friction proportional to the velocity of the mass with proportionality constant 20 Ns/m. a. 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 an external force of F(t) = 10 sin t is applied to the mass-spring system. Setup and solve the new model for the position of the spring as a function of time.
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
Transcribed Image Text: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
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