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Simple_harmonic_oscillator.gif(116 × 359 piksel, fayl həcmi: 52 KB, MIME növü: image/gif, ilmələnib, 15 çərçivə, 1,1 s)
 | Bu fayl Vikianbarda yerləşir. Açıqlama səhifəsindəki məlumatlar aşağıda göstərilib. Vikianbar azad lisenziyalı media anbarıdır. Siz də töhfə verə bilərsiniz. |
| İzah | Illustration of a en:Simple harmonic oscillator |
| Tarix | |
| Mənbə | self-made with en:Matlab. Converted to gif animation with the en:ImageMagick convert tool (see the specific command later in the code). |
| Müəllif | Oleg Alexandrov |
| Digər versiyalar | Damped spring.gif:  Damped version |
| GIF genesis |  This diagram was created with MATLAB. |
| Mənbə kodu | MATLAB codefunction 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 right 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 |
 | Mən, bu əsərin müəllif hüquqlarının sahibi kimi, əsəri ictimai mülkiyyətə buraxıram. Bu icazə bütün dünyada qüvvədədir. In some countries this may not be legally possible; if so: Mən hər kəsə bu əsərdən hər hansı bir məqsəd üçün, heç bir şərt olmadan, qanunla belə şərtlər tələb olunmadığı təqdirdə istifadə etmək hüququnu verirəm. |
| Annotations | This image is annotated: View the annotations at Commons |
Faylın tarixçəsi
Faylın əvvəlki versiyasını görmək üçün gün/tarix bölməsindəki tarixlərə klikləyin.
| Tarix/Vaxt | Miniatür | Ölçülər | İstifadəçi | Şərh | |
|---|---|---|---|---|---|
| hal-hazırkı | 03:12, 24 iyun 2007 |  | 116 × 359 (52 KB) | tweak | |
| 03:10, 24 iyun 2007 |  | 157 × 362 (51 KB) | Reverted to earlier revision | ||
| 03:10, 24 iyun 2007 |  | 116 × 359 (7 KB) | tweak | ||
| 02:42, 24 iyun 2007 |  | 157 × 362 (51 KB) | {{Information |Description= |Source=self-made with en:Matlab. Converted to gif animation with the en:ImageMagik convert tool. |Date= ~~~~~ |Author= }} {{PD-self}} |
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Fayl Faylin tarixcesi Faylin istifadesi Faylin qlobal istifadesiDaha yuksek versiyasi yoxdur Simple harmonic oscillator gif 116 359 piksel fayl hecmi 52 KB MIME novu image gif ilmelenib 15 cercive 1 1 s Bu fayl Vikianbarda yerlesir Aciqlama sehifesindeki melumatlar asagida gosterilib Vikianbar azad lisenziyali media anbaridir Siz de tohfe vere bilersiniz IzahSimple harmonic oscillator gif Illustration of a en Simple harmonic oscillator Tarix 24 iyun 2007 02 42 Menbe self made with en Matlab Converted to gif animation with the en ImageMagick convert tool see the specific command later in the code Muellif Oleg Alexandrov Diger versiyalar Damped spring gif nbsp Damped version GIF nbsp genesisInfoField nbsp This diagram was created with MATLAB Menbe koduInfoFieldMATLAB code 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 right 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 Public domain Public domain false false Men bu eserin muellif huquqlarinin sahibi kimi eseri ictimai mulkiyyete buraxiram Bu icaze butun dunyada quvvededir In some countries this may not be legally possible if so Men her kese bu eserden her hansi bir meqsed ucun hec bir sert olmadan qanunla bele sertler teleb olunmadigi teqdirde istifade etmek huququnu verirem AnnotationsInfoFieldThis image is annotated View the annotations at Commons84 321 8 8 116 359 gysdo8sBasliqlarazerbaycancaBu faylin neyi temsil etdiyine dair bir setirlik izahat elave etBu faylda tesvir olunan elementlertesvir ediryaradiciVikidata elementi olmayan bir nece deyermuellifin qisa adi Oleg AlexandrovVikimedia istifadeci adi Oleg AlexandrovURL https commons wikimedia org wiki user Oleg Alexandrovcopyright status nbsp ingilismuellif huquqlari ile qorunur lakin muellif huquqlarinin sahibi terefinden ictimai istifadeye verilmisdirlisenziyareleased into the public domain by the copyright holder nbsp ingilisyaranma tarixi24 iyun 2007media type nbsp ingilisimage gif Faylin tarixcesi Faylin evvelki versiyasini gormek ucun gun tarix bolmesindeki tarixlere klikleyin Tarix VaxtMiniaturOlculerIstifadeciSerh hal hazirki03 12 24 iyun 2007116 359 52 KB Oleg Alexandrovtweak 03 10 24 iyun 2007157 362 51 KB Oleg AlexandrovReverted to earlier revision 03 10 24 iyun 2007116 359 7 KB Oleg Alexandrovtweak 02 42 24 iyun 2007157 362 51 KB Oleg Alexandrov Information Description Source self made with en Matlab Converted to gif animation with the en ImageMagik convert tool Date Author Oleg Alexandrov PD self Faylin istifadesi Asagidaki sehife bu fayli istifade edir Yirgalanma Faylin qlobal istifadesi Bu fayl asagidaki vikilerde istifade olunur am wikipedia org layihesinde istifadesi አቅም ar wikipedia org layihesinde istifadesi هزاز توافقي حركة فيزياء حركة توافقية بسيطة تذبذب فيزياء حمل متحرك نسبة الاضمحلال ast wikipedia org layihesinde istifadesi Movimientu beta wikiversity org layihesinde istifadesi Chuyển động Dao động Song dao động lo xo Song dao động lo xo len xuống Dao động lo xo Song dao động Dao động lo xo dọc Cac chuyển động cơ bản bn wikipedia org layihesinde istifadesi স পন দন গত bs wikipedia org layihesinde istifadesi Sinusoida ca wikipedia org layihesinde istifadesi Moviment harmonic simple Sinusoide Oscil lacio cs wikipedia org layihesinde istifadesi Kmitani Oscilator Ekviparticni teorem cv wikipedia org layihesinde istifadesi Sullanusem Garmonille oscillyator cy wikipedia org layihesinde istifadesi Mudiant Osgiliadur harmonig da wikipedia org layihesinde istifadesi Oscillator de wikibooks org layihesinde istifadesi Entropie Zeit Physik Oberstufe Schwingungen und Wellen Mechanische Schwingungen el wikipedia org layihesinde istifadesi Nomos toy Xoyk Aplh armonikh talantwsh en wikipedia org layihesinde istifadesi User Oleg Alexandrov Pictures Talk Vibration User Bci2 Vibration Effective mass spring mass system User Bci2 Books Wk2Book User Bci2 Books Wk3vol1 User Bci2 Books Wk4 Talk Molecular models of DNA Galleries User Support and Defend chain rule Wikipedia Featured picture candidates May 2011 Wikipedia Featured picture candidates Simple harmonic oscillator en wikibooks org layihesinde istifadesi Calculus Print version Physics Course Oscillation Calculus Chain Rule Physics Course Oscillation Oscillation Up and Down Engineering Handbook Oscillation Bu faylin qlobal istifadesine baxin Menbe https az wikipedia org wiki Fayl Simple harmonic oscillator gif