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| Keywords: Simple harmonic oscillator.gif Illustration of a en Simple harmonic oscillator self-made with en Matlab Converted to gif animation with the en ImageMagick convert tool see the specific command later in the code 02 42 24 June 2007 UTC Oleg Alexandrov 49pxDamped version Created with MATLAB Source code <source lang matlab > function main colors red 0 867 0 06 0 14; blue 0 129 205/256; green 0 200 70/256; black 0 0 0; white 1 1 1 0 99; cardinal 196 30 58/256; cerulean 0 123 167/256; denim 21 96 189/256; cobalt 0 71 171/256; pblue 0 49 83/256; teracotta 226 114 91/256; tene 205 87 0/256; wall_color pblue; spring_color cobalt; mass_color tene; a 0 65; bmass_color a mass_color+ 1-a black; linewidth and fontsize lw 2; fs 20; ww 0 5; wall width ms 0 25; the size of the mass sw 0 1; spring width curls 8; A 0 2; the amplitude of spring oscillations B -1; the y coordinate of the base state the origin is higher at the wall Each of the small lines has length l l 0 05; N 15; times per oscillation No 1; number of oscillations for i 1 N No set up the plotting window figure 1 ; clf; hold on; axis equal; axis off; t 2 pi i-1 / N-0 +pi/2; current time H A sin t + B; position of the mass plot the spring from Start to End Start 0 0; End 0 H; X Y do_plot_spring Start End curls sw ; plot X Y 'linewidth' lw 'color' spring_color ; Here we cheat We modify the point B so that the mass is attached exactly at the end of the spring This should not be necessary I am too lazy to to the exact calculation K length X ; End 1 X K ; End 2 Y K ; plot the wall from which the spring is hanging plot_wall -ww/2 ww/2 l lw wall_color ; plot the mass at the end of the spring X -ms/2 ms/2 ms/2 -ms/2 -ms/2 ms/2+End 1 ; Y 0 0 -ms -ms 0 0+End 2 ; H fill X Y mass_color 'EdgeColor' bmass_color 'linewidth' lw ; the bounding box Sx -0 4 ww; Sy B-A-ms+0 05; Lx 0 4 ww+l; Ly l; axis Sx Lx Sy Ly ; plot Sx Sy ' ' 'color' white ; a hack to avoid a saveas to eps bug saveas gcf sprintf 'Spring_frame d eps' 1000+i 'psc2' save the current frame disp sprintf 'Spring_frame d' 1000+i ; show the frame number we are at pause 0 1 ; end The following command was used to create the animated figure convert -antialias -loop 10000 -delay 7 -compress LZW Spring_frame10 Simple_harmonic_oscillator gif function X Y do_plot_spring A B curls sw ; plot a 3D spring then project it onto 2D theta controls the angle of projection The string starts at A and ends at B will rotate by theta when projecting from 1D to 2D theta pi/6; Npoints 500; spring length D sqrt A 1 -B 1 2+ A 2 -B 2 2 ; X linspace 0 1 Npoints ; XX linspace -pi/2 2 pi curls+pi/2 Npoints ; Y -sw cos XX ; Z sw sin XX ; b gives the length of the small straight segments at the ends of the spring to which the wall and the mass are attached b 0 05; stretch the spring in X to make it of length D - 2 b N length X ; X D-2 b X-X 1 / X N -X 1 ; shift by b to the rigth and add the two small segments of length b X 0 X+b X N +2 b; Y Y 1 Y Y N ; Z Z 1 Z Z N ; project the 3D spring to 2D M cos theta sin theta ; -sin theta cos theta ; N length X ; for i 1 N; V M X i Z i '; X i V 1 ; Z i V 2 ; end shift the spring to start from 0 X X-X 1 ; now that we have the horisontal spring X Y of length D rotate and translate it to go from A to B Theta atan2 B 2 -A 2 B 1 -A 1 ; M cos Theta -sin Theta ; sin Theta cos Theta ; N length X ; for i 1 N; V M X i Y i '+A'; X i V 1 ; Y i V 2 ; end function plot_wall S E l lw wall_color Plot a wall from S to E no 20; spacing E-S / no-1 ; plot S E 0 0 'linewidth' 1 8 lw 'color' wall_color ; V l 0 0 1 1 ; for i 0 no-1 plot S+ i spacing + V V 'color' wall_color end </source> Animations of vibrations and waves Files by User Oleg Alexandrov from en wikipedia Animated GIF Mass-spring systems Images with Matlab source code | ||||
