Finding the Transfer Function of a MassSpringDamper System Example

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This problem is adapted form a textbook problem that gave me lot of trouble the first time I tried it. It is pretty long, but I think it has a lot of important concepts in it. • Timestamps: • 00:00 - Problem introduction and coordinate definitions • 01:20 - Free body diagrams and dynamic modeling • 13:20 - Laplace Transform • 20:07 - Solving system of equations (Cramer's Rule) • 40:18 - Finding transfer function • 41:55 - Answer • MATLAB code to solve system of equations: • % -------------------------------------------------------------------------------------------------- • % Requires Symbolic Toolbox! • syms s F % set up symbolic variables • A = [10*s^2+3*s+2 -2 -3*s; 2 -7-5*s^2 5; 3*s 5 -3*s-5]; % A matrix (coefficients) • b = [F;0;0]; % b matrix (Right hand sides) • X = A\\b; % Solve for x vector by multiplying b by the inverse of A • X2 = X(2); % X2 is the second element in our X vector • TF = simplify(X2/F) % transfer funciton is output over input • % -------------------------------------------------------------------------------------------------- • If you have any questions or want to see me make a video about something, feel free to leave a comment below! • Errata: • The problem statement has position misspelled as positon

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