Code covered by the BSD License

# Using Analytical Tools to Gain Insight and Speed-up Num. Analysis in MATLAB & Symbolic Math Toolbox

### Deepak Ramaswamy (view profile)

28 Jan 2013 (Updated )

files from the webinar

```%% Begin README: Mass Spring Damper
% The <http://www.mathworks.com/products/symbolic/description5.html Symbolic Math Notebook app>
% and the <http://www.mathworks.com/products/symbolic/index.html Symbolic Math Toolbox> are
% demonstrated using a mass spring damper example. The example is simple
% but gives a flavor of the capabilities of the toolbox.
%
% <<image/image.PNG>>
%
%
% Copyright 2012 The MathWorks, Inc.
%% References
%
% * Find the related webinar: *Using Analytical Tools to Gain Insight and Speed Up
%  Numerical Analysis in MATLAB* <http://www.mathworks.com/wbnr73465 here>

%% Mass spring damper solved in the Symbolic Math Notebook - I
% The analytical solution is <http://www.mathworks.com/help/symbolic/mupad_ref/ode-solve.html derived> first, followed by the critical
% damping case using the <http://www.mathworks.com/help/symbolic/mupad_ref/limit.html limit> function.
% The system is then solved in the <http://www.mathworks.com/help/symbolic/mupad_ref/laplace.html Laplace> domain. Finally
% the phase plot is obtained.
%
% <matlab:open('massspringdamper.mn') Open notebook>

%% Mass spring damper solved in the Symbolic Math Notebook - II
% This takes another look at the mass spring damper by plotting the time
% and frequency plots for a specific case and includes an animation.
%
% <matlab:open('MSD.mn') Open notebook>

%% Mass spring damper solved using Symbolic in MATLAB
% The <http://www.mathworks.com/help/symbolic/eig.html eigenvalues> are extracted by converting to a first order system. Then
% the <http://www.mathworks.com/help/symbolic/poles.html poles> are derived. it is shown that the poles are exactly identical
% and since the real parts of the eigenvalues/poles are always negative,
% the system is always stable.
%
% <matlab:open('massspringdamper.m') Open script>
%
% <matlab:massspringdamper Run script>```