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Unformatted text preview: Outline Look Back at Utility Matrices in MATLAB What is a SpringMass System ? Why are SpringMass Systems Important ? Lets talk about a special matrix K Very Short Introduction to SpringMass Systems Session 1: Examples and Idea of a Toeplitz Matrix Dr. Kartik V. Bulusu & Prof. Michael W. Plesniak Department of Mechanical and Aerospace Engineering MAE 1002  Spring 2011 February 9, 2011 Dr. Kartik V. Bulusu & Prof. Michael W. Plesniak Very Short Introduction to SpringMass Systems Outline Look Back at Utility Matrices in MATLAB What is a SpringMass System ? Why are SpringMass Systems Important ? Lets talk about a special matrix K Look Back at Utility Matrices in MATLAB What is a SpringMass System ? Why are SpringMass Systems Important ? Example: Modeling of Large Scale Structures Example: Modeling of Vehicle Suspension Systems Example: Cardiac Surgery Simulation and Tissue Deformation Example: Acoustic Insulation of Automotive and Home Appliances Two Interesting Pieces of Physics (N) Springs (N1) Mass Systems Lets talk about a special matrix K Key Idea #1: Toeplitz Matrices Determinant of square matrix K Dr. Kartik V. Bulusu & Prof. Michael W. Plesniak Very Short Introduction to SpringMass Systems Outline Look Back at Utility Matrices in MATLAB What is a SpringMass System ? Why are SpringMass Systems Important ? Lets talk about a special matrix K Look Back at Utility Matrices I eye(m,n) returns an m by n matrix with 1s on the main diagonal I zeros(m,n) returns an m by n matrix with zeroes I ones(m,n) returns an m by n matrix with zeroes I rand(m,n) returns an m by n matrix of random numbers between 0 and 1 I diag(v) creates a matrix with vector v on the diagonal I diag(A) creates a vector with the diagonal of matrix A Dr. Kartik V. Bulusu & Prof. Michael W. Plesniak Very Short Introduction to SpringMass Systems Outline Look Back at Utility Matrices in MATLAB What is a SpringMass System ? Why are SpringMass Systems Important ? Lets talk about a special matrix K What is a SpringMass System ? In classical mechanics, a harmonic oscillator (for eg., springmass system) is a system which, when displaced from its equilibrium position, experiences a restoring force, F, proportional to the displacement, x: F = kx , where k is positive constant (spring constant) [ Click on the images to view animations ] Source of animations: Site maintained by David M. Harrison for Department of Physics, University of Toronto Dr. Kartik V. Bulusu & Prof. Michael W. Plesniak Very Short Introduction to SpringMass Systems Outline Look Back at Utility Matrices in MATLAB What is a SpringMass System ? Why are SpringMass Systems Important ? Lets talk about a special matrix K Example: Modeling of Large Scale Structures Example: Modeling of Vehicle Suspension Systems Example: Cardiac Surgery Simulation and Tissue Deformation Example: Acoustic Insulation of Automotive and Home Appliance Two Interesting Pieces of Physics (N) Springs (N1) Mass Systems...
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