Concept explainers
Find the rank of the controllability matrix for the four mass system in all of the cases that a single control is applied to each of the four masses and compare your results with the conclusions obtained in Problem 4. (Note that by symmetry considerations, it is only necessary to consider one of the masses on the end and one of the interior masses.)
Repeat Problem 2 for a system of four masses connected by springs. Give a physical interpretation of the normal modes of vibration. Does the normal mode representation rule out complete controllability for the case of a scalar control applied to any single mass? Explain.
Want to see the full answer?
Check out a sample textbook solutionChapter 6 Solutions
Differential Equations: An Introduction to Modern Methods and Applications
Additional Math Textbook Solutions
Introductory Statistics
A First Course in Probability (10th Edition)
Basic Business Statistics, Student Value Edition
Algebra and Trigonometry (6th Edition)
STATISTICS F/BUSINESS+ECONOMICS-TEXT
Intro Stats, Books a la Carte Edition (5th Edition)
- No chatgpt pls will upvotearrow_forwardWhich degenerate conic is formed when a double cone is sliced through the apex by a plane parallel to the slant edge of the cone?arrow_forwardFor the problem below, what are the possible solutions for x? Select all that apply. 2 x²+8x +11 = 0 x2+8x+16 = (x+4)² = 5 1116arrow_forward
- For the problem below, what are the possible solutions for x? Select all that apply. x² + 12x - 62 = 0 x² + 12x + 36 = 62 + 36 (x+6)² = 98arrow_forwardSelect the polynomials below that can be solved using Completing the Square as written. 6m² +12m 8 = 0 Oh²-22x 7 x²+4x-10= 0 x² + 11x 11x 4 = 0arrow_forwardProve that the usual toplogy is firast countble or hot and second countble. ①let cofinte toplogy onx show that Sivast countble or hot and second firast. 3) let (x,d) be matricspace show that is first and second countble. 6 Show that Indiscret toplogy is firstand Second op countble or not.arrow_forward
- H.W For any events A and B, show that 1. P(AB)s P(A)≤ P(AUB)≤ P(A) + P(B)arrow_forwarda) Find the scalars p, q, r, s, k1, and k2. b) Is there a different linearly independent eigenvector associated to either k1 or k2? If yes,find it. If no, briefly explain.arrow_forwardPlz no chatgpt answer Plz Will upvotearrow_forward
- 1/ Solve the following: 1 x + X + cos(3X) -75 -1 2 2 (5+1) e 5² + 5 + 1 3 L -1 1 5² (5²+1) 1 5(5-5)arrow_forwardI need expert handwritten solution.to this integralarrow_forwardHow to understand and learn Laurent's serial and what's the point of Laurent's serial And what are the steps of a smooth solution for Laurentarrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage