added lecture 15

HW4/README.md

@@ -1,4 +1,4 @@
-# Homework #3
+# Homework #4
 ## due 3/1/17 by 11:59pm
 
 

lecture_15/.ipynb_checkpoints/lecture_15-checkpoint.ipynb

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+{
+ "cells": [],
+ "metadata": {},
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

lecture_15/animate_eig.m

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+function [v,e]=animate_eig(k,m)
+  % create a series of png's for use in an animation based on 
+  % spring constants [k1,k2,k3]=k
+  % and
+  % masses 
+  % [m1,m2]=m
+
+  % check inputs for m and k
+  if length(m)==1
+    m1=m;
+    m2=m;
+  else
+    m1=m(1);
+    m2=m(2);
+  end
+  if length(k)==1
+    k1=k; k2=k; k3=k;
+  else
+    k1=k(1);
+    k2=k(2);
+    k3=k(3);
+  end
+  setdefaults
+  K=[k1/m1+k2/m1,-k2/m1;-k3/m2,k2/m2+k3/m2];
+  [v,e]=eig(K);
+  w1=e(1,1); w2=e(2,2);
+  scale = 0.5; % the magnitude of oscillations is not important for vibrational modes
+               % just set scale to 1/2 for nice plots
+               % the eigenvector magnitude is independent of the solution
+  X11=v(1,1)*scale; X12=v(2,1)*scale;
+  X21=v(1,2)*scale; X22=v(2,2)*scale;
+  f11=@(t) X11*sin(w1*t); f12=@(t) X12*sin(w1*t);
+  f21=@(t) X21*sin(w2*t); f22=@(t) X22*sin(w2*t);
+  f=figure();
+  time=linspace(-1,4);
+  % create a loop to plot the position over time where mass 1 and 2 start at x=1 and x=2 m
+  % then for the next vibrational mode, mass 1 and 2 start at x=3 and x=4 m
+
+  for i=1:length(time)
+    t=time(i);
+    plot(f11(t)+1,0,'rs',f11(time+t)+1,-time,...
+    f12(t)+2,0,'rs',f12(time+t)+2,-time,...
+    f21(t)+3,0,'bo',f21(time+t)+3,-time,...
+    f22(t)+4,0,'bo',f22(time+t)+4,-time)
+    axis([0 6 -4 1])
+    title('Vibration Modes')
+    xlabel('position (m)')
+    ylabel('time (s)')
+    filename=sprintf('output/%05d.png',i);
+    % another option for saving a plot to a png is the 'print' command
+    print(filename)
+  end
+  % this is a system command to use ImageMagick's cli 'convert' to create an animated gif
+  % if you don't have ImageMagick installed, comment this next line
+  system ("convert -delay 10 -loop 0 output/*png eigenvalues.gif")
+end