Commit 695d534d authored by Yassine's avatar Yassine
Browse files

latex yeet

parent 019383d9
......@@ -71,6 +71,16 @@
\@writefile{toc}{\contentsline {paragraph}{Caractérisation du signal Vdistance(t):}{8}{section*.5}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {12}{\ignorespaces Capteur Lidar POL4071}}{9}{figure.12}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Le 555 Astable}{9}{section*.6}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {4}Partie Mathématiques}{10}{section.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {4.1}Semaine 1}{10}{subsection.4.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {4.1.1}Pourquoi les systèmes vus en ZG étaient descriptibles par des équations différentielles ?}{10}{subsubsection.4.1.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {3.2.2}Temps 2}{10}{subsubsection.3.2.2}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Activité 1}{10}{section*.7}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Activité 3}{10}{section*.8}\protected@file@percent }
\@writefile{toc}{\contentsline {paragraph}{Activité 4}{10}{section*.9}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {4}Partie Mathématiques}{11}{section.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {4.1}Semaine 1}{11}{subsection.4.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {4.1.1}Pourquoi les systèmes vus en ZG étaient descriptibles par des équations différentielles ?}{11}{subsubsection.4.1.1}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {13}{\ignorespaces Tableau d'analogie Mécanique/Électrique}}{12}{figure.13}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {5}Résolution numérique}{12}{section.5}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {6}Synthèse}{12}{section.6}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {6.1}Similarités théorique (calculées lor de la première activité)}{12}{subsection.6.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {6.2}Similarités lors de l’expérimentation}{12}{subsection.6.2}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {7}Bibliographie}{12}{section.7}\protected@file@percent }
......@@ -18,3 +18,4 @@
\contentsline {figure}{\numberline {10}{\ignorespaces Régime critique}}{8}{figure.10}%
\contentsline {figure}{\numberline {11}{\ignorespaces Régime apériodique}}{8}{figure.11}%
\contentsline {figure}{\numberline {12}{\ignorespaces Capteur Lidar POL4071}}{9}{figure.12}%
\contentsline {figure}{\numberline {13}{\ignorespaces Tableau d'analogie Mécanique/Électrique}}{12}{figure.13}%
This is pdfTeX, Version 3.14159265-2.6-1.40.20 (TeX Live 2019/Debian) (preloaded format=pdflatex 2022.4.25) 2 JUN 2022 13:07
This is pdfTeX, Version 3.14159265-2.6-1.40.20 (TeX Live 2019/Debian) (preloaded format=pdflatex 2022.4.25) 3 JUN 2022 13:53
entering extended mode
restricted \write18 enabled.
%&-line parsing enabled.
......@@ -704,7 +704,7 @@ LaTeX Info: Redefining \nameref on input line 25.
* (1in=72.27pt=25.4mm, 1cm=28.453pt)
\c@lstlisting=\count329
<images/enib_logo.png, id=64, 84.5559pt x 43.8438pt>
<images/enib_logo.png, id=88, 84.5559pt x 43.8438pt>
File: images/enib_logo.png Graphic file (type png)
<use images/enib_logo.png>
Package pdftex.def Info: images/enib_logo.png used on input line 29.
......@@ -714,7 +714,7 @@ Overfull \hbox (22.129pt too wide) in paragraph at lines 29--30
[][]
[]
<images/premiere_image.png, id=65, 1204.5pt x 652.4375pt>
<images/premiere_image.png, id=89, 1204.5pt x 652.4375pt>
File: images/premiere_image.png Graphic file (type png)
<use images/premiere_image.png>
Package pdftex.def Info: images/premiere_image.png used on input line 61.
......@@ -821,38 +821,38 @@ Underfull \hbox (badness 10000) in paragraph at lines 109--110
[]
<images/cr1/ihm.jpg, id=127, 1878.01625pt x 1758.57pt>
<images/cr1/ihm.jpg, id=159, 1878.01625pt x 1758.57pt>
File: images/cr1/ihm.jpg Graphic file (type jpg)
<use images/cr1/ihm.jpg>
Package pdftex.def Info: images/cr1/ihm.jpg used on input line 113.
(pdftex.def) Requested size: 169.01416pt x 158.26447pt.
<images/cr1/mesures.png, id=128, 1537.745pt x 2055.68pt>
<images/cr1/mesures.png, id=160, 1537.745pt x 2055.68pt>
File: images/cr1/mesures.png Graphic file (type png)
<use images/cr1/mesures.png>
Package pdftex.def Info: images/cr1/mesures.png used on input line 114.
(pdftex.def) Requested size: 123.02211pt x 164.45776pt.
<images/cr1/forme.png, id=129, 807.015pt x 575.14874pt>
<images/cr1/forme.png, id=161, 807.015pt x 575.14874pt>
File: images/cr1/forme.png Graphic file (type png)
<use images/cr1/forme.png>
Package pdftex.def Info: images/cr1/forme.png used on input line 115.
(pdftex.def) Requested size: 201.75325pt x 143.78683pt.
<images/cr1/results_masse.png, id=130, 642.4pt x 481.8pt>
<images/cr1/results_masse.png, id=162, 642.4pt x 481.8pt>
File: images/cr1/results_masse.png Graphic file (type png)
<use images/cr1/results_masse.png>
Package pdftex.def Info: images/cr1/results_masse.png used on input line 122.
(pdftex.def) Requested size: 224.84337pt x 168.63252pt.
<images/cr1/results_liquide.png, id=131, 642.4pt x 481.8pt>
<images/cr1/results_liquide.png, id=163, 642.4pt x 481.8pt>
File: images/cr1/results_liquide.png Graphic file (type png)
<use images/cr1/results_liquide.png>
Package pdftex.def Info: images/cr1/results_liquide.png used on input line 123
.
(pdftex.def) Requested size: 224.84337pt x 168.63252pt.
<images/cr1/results_k.png, id=132, 642.4pt x 481.8pt>
<images/cr1/results_k.png, id=164, 642.4pt x 481.8pt>
File: images/cr1/results_k.png Graphic file (type png)
<use images/cr1/results_k.png>
Package pdftex.def Info: images/cr1/results_k.png used on input line 124.
(pdftex.def) Requested size: 224.84337pt x 168.63252pt.
<images/cr1/results_piston.png, id=133, 642.4pt x 481.8pt>
<images/cr1/results_piston.png, id=165, 642.4pt x 481.8pt>
File: images/cr1/results_piston.png Graphic file (type png)
<use images/cr1/results_piston.png>
Package pdftex.def Info: images/cr1/results_piston.png used on input line 125.
......@@ -875,7 +875,7 @@ l.129 O
<./images/cr1/ihm.jpg> <./images/cr1/mesures.png> <./images/cr1/forme.png> <./
images/cr1/results_masse.png> <./images/cr1/results_liquide.png> <./images/cr1/
results_k.png> <./images/cr1/results_piston.png>]
<images/cr1/rlc.png, id=161, 513.92pt x 372.39125pt>
<images/cr1/rlc.png, id=194, 513.92pt x 372.39125pt>
File: images/cr1/rlc.png Graphic file (type png)
<use images/cr1/rlc.png>
Package pdftex.def Info: images/cr1/rlc.png used on input line 141.
......@@ -885,7 +885,7 @@ Underfull \hbox (badness 10000) in paragraph at lines 137--143
[]
<images/cr1/circuit.png, id=162, 1105.88156pt x 587.19376pt>
<images/cr1/circuit.png, id=195, 1105.88156pt x 587.19376pt>
File: images/cr1/circuit.png Graphic file (type png)
<use images/cr1/circuit.png>
Package pdftex.def Info: images/cr1/circuit.png used on input line 147.
......@@ -918,7 +918,7 @@ Underfull \hbox (badness 10000) in paragraph at lines 155--156
[]
<images/cr1/cablage.png, id=170, 1355.8153pt x 1035.87pt>
<images/cr1/cablage.png, id=202, 1355.8153pt x 1035.87pt>
File: images/cr1/cablage.png Graphic file (type png)
<use images/cr1/cablage.png>
Package pdftex.def Info: images/cr1/cablage.png used on input line 161.
......@@ -928,12 +928,12 @@ Overfull \hbox (21.07654pt too wide) in paragraph at lines 161--162
[][]
[]
<images/cr1/decharge.png, id=171, 998.22937pt x 795.72281pt>
<images/cr1/decharge.png, id=203, 998.22937pt x 795.72281pt>
File: images/cr1/decharge.png Graphic file (type png)
<use images/cr1/decharge.png>
Package pdftex.def Info: images/cr1/decharge.png used on input line 166.
(pdftex.def) Requested size: 209.63435pt x 167.10672pt.
<images/cr1/jeux.png, id=172, 671.50874pt x 375.4025pt>
<images/cr1/jeux.png, id=204, 671.50874pt x 375.4025pt>
File: images/cr1/jeux.png Graphic file (type png)
<use images/cr1/jeux.png>
Package pdftex.def Info: images/cr1/jeux.png used on input line 174.
......@@ -975,7 +975,7 @@ Underfull \hbox (badness 10000) in paragraph at lines 188--189
[]
<images/cr1/pseudo_periodique.png, id=181, 1901.1025pt x 408.52625pt>
<images/cr1/pseudo_periodique.png, id=213, 1901.1025pt x 408.52625pt>
File: images/cr1/pseudo_periodique.png Graphic file (type png)
<use images/cr1/pseudo_periodique.png>
Package pdftex.def Info: images/cr1/pseudo_periodique.png used on input line 1
......@@ -986,7 +986,7 @@ Underfull \hbox (badness 10000) in paragraph at lines 202--203
[]
<images/cr1/periodique.png, id=182, 1903.11pt x 409.53pt>
<images/cr1/periodique.png, id=214, 1903.11pt x 409.53pt>
File: images/cr1/periodique.png Graphic file (type png)
<use images/cr1/periodique.png>
Package pdftex.def Info: images/cr1/periodique.png used on input line 226.
......@@ -998,17 +998,17 @@ has been already used, duplicate ignored
\fi \fi
l.229
<./images/cr1/pseudo_periodique.png>]
<images/cr1/critique.png, id=190, 1901.1025pt x 412.54124pt>
<images/cr1/critique.png, id=222, 1901.1025pt x 412.54124pt>
File: images/cr1/critique.png Graphic file (type png)
<use images/cr1/critique.png>
Package pdftex.def Info: images/cr1/critique.png used on input line 241.
(pdftex.def) Requested size: 475.27446pt x 103.13506pt.
<images/cr1/aperiodique.png, id=191, 1906.12125pt x 414.54875pt>
<images/cr1/aperiodique.png, id=223, 1906.12125pt x 414.54875pt>
File: images/cr1/aperiodique.png Graphic file (type png)
<use images/cr1/aperiodique.png>
Package pdftex.def Info: images/cr1/aperiodique.png used on input line 256.
(pdftex.def) Requested size: 476.52914pt x 103.63693pt.
<images/demarche 1/capteur.png, id=192, 740.7675pt x 378.41376pt>
<images/demarche 1/capteur.png, id=224, 740.7675pt x 378.41376pt>
File: images/demarche 1/capteur.png Graphic file (type png)
<use images/demarche 1/capteur.png>
Package pdftex.def Info: images/demarche 1/capteur.png used on input line 272.
......@@ -1034,37 +1034,37 @@ e{figure.11}) has been already used, duplicate ignored
l.276 \noindent
<./images/cr1/periodique.png> <./images/cr1/critique.png> <./im
ages/cr1/aperiodique.png>]
<images/demarche 1/astable.png, id=202, 427.5975pt x 345.29pt>
<images/demarche 1/astable.png, id=234, 427.5975pt x 345.29pt>
File: images/demarche 1/astable.png Graphic file (type png)
<use images/demarche 1/astable.png>
Package pdftex.def Info: images/demarche 1/astable.png used on input line 284.
(pdftex.def) Requested size: 171.03596pt x 138.11354pt.
<images/demarche 1/sortie_astable.png, id=203, 1239.63126pt x 456.70625pt>
<images/demarche 1/sortie_astable.png, id=235, 1239.63126pt x 456.70625pt>
File: images/demarche 1/sortie_astable.png Graphic file (type png)
<use images/demarche 1/sortie_astable.png>
Package pdftex.def Info: images/demarche 1/sortie_astable.png used on input li
ne 285.
(pdftex.def) Requested size: 347.09439pt x 127.87688pt.
<images/demarche 1/mesure_ta.png, id=204, 225.09094pt x 161.85469pt>
<images/demarche 1/mesure_ta.png, id=236, 225.09094pt x 161.85469pt>
File: images/demarche 1/mesure_ta.png Graphic file (type png)
<use images/demarche 1/mesure_ta.png>
Package pdftex.def Info: images/demarche 1/mesure_ta.png used on input line 29
3.
(pdftex.def) Requested size: 157.56258pt x 113.2975pt.
<images/demarche 1/curseurs_ta.png, id=205, 627.84563pt x 342.5297pt>
<images/demarche 1/curseurs_ta.png, id=237, 627.84563pt x 342.5297pt>
File: images/demarche 1/curseurs_ta.png Graphic file (type png)
<use images/demarche 1/curseurs_ta.png>
Package pdftex.def Info: images/demarche 1/curseurs_ta.png used on input line
295.
(pdftex.def) Requested size: 251.13379pt x 137.00945pt.
<images/demarche 1/mesure_tb.png, id=206, 223.58531pt x 169.38281pt>
<images/demarche 1/mesure_tb.png, id=238, 223.58531pt x 169.38281pt>
File: images/demarche 1/mesure_tb.png Graphic file (type png)
<use images/demarche 1/mesure_tb.png>
Package pdftex.def Info: images/demarche 1/mesure_tb.png used on input line 30
3.
(pdftex.def) Requested size: 156.50864pt x 118.56714pt.
<images/demarche 1/curseurs_tb.png, id=207, 344.78813pt x 344.78813pt>
<images/demarche 1/curseurs_tb.png, id=239, 344.78813pt x 344.78813pt>
File: images/demarche 1/curseurs_tb.png Graphic file (type png)
<use images/demarche 1/curseurs_tb.png>
Package pdftex.def Info: images/demarche 1/curseurs_tb.png used on input line
......@@ -1081,33 +1081,75 @@ png> <./images/demarche 1/sortie_astable.png> <./images/demarche 1/mesure_ta.pn
g> <./images/demarche 1/curseurs_ta.png>]
LaTeX Font Info: External font `lmex10' loaded for size
(Font) <17.28> on input line 312.
Underfull \hbox (badness 10000) in paragraph at lines 318--320
[]
Overfull \hbox (21.7287pt too wide) in paragraph at lines 333--334
[][]
[]
Underfull \hbox (badness 10000) in paragraph at lines 336--337
[]
[10 <./images/demarche 1/mesure_tb.png> <./images/demarche 1/curseurs_tb.png>]
File: images/cr1/rlc.png Graphic file (type png)
<use images/cr1/rlc.png>
Package pdftex.def Info: images/cr1/rlc.png used on input line 336.
Package pdftex.def Info: images/cr1/rlc.png used on input line 363.
(pdftex.def) Requested size: 154.17719pt x 111.71823pt.
[10 <./images/demarche 1/mesure_tb.png> <./images/demarche 1/curseurs_tb.png>]
Package atveryend Info: Empty hook `BeforeClearDocument' on input line 342.
[11]
Package atveryend Info: Empty hook `AfterLastShipout' on input line 342.
[11]
Underfull \hbox (badness 10000) in paragraph at lines 399--400
[]
Underfull \hbox (badness 10000) in paragraph at lines 401--402
[]
Underfull \hbox (badness 10000) in paragraph at lines 403--404
[]
Underfull \hbox (badness 10000) in paragraph at lines 410--413
[]
Package atveryend Info: Empty hook `BeforeClearDocument' on input line 415.
[12pdfTeX warning (ext4): destination with the same identifier (name{figure.13}
) has been already used, duplicate ignored
\AtBegShi@Output ...ipout \box \AtBeginShipoutBox
\fi \fi
l.415 \end{document}
]
Package atveryend Info: Empty hook `AfterLastShipout' on input line 415.
(./compte_rendu_zg2.aux)
Package atveryend Info: Executing hook `AtVeryEndDocument' on input line 342.
Package atveryend Info: Executing hook `AtEndAfterFileList' on input line 342.
Package atveryend Info: Executing hook `AtVeryEndDocument' on input line 415.
Package atveryend Info: Executing hook `AtEndAfterFileList' on input line 415.
Package rerunfilecheck Info: File `compte_rendu_zg2.out' has not changed.
(rerunfilecheck) Checksum: 123EAE3A781778E4A600D2F8260774C2;1234.
(rerunfilecheck) Checksum: C978CF39EE20124DEC0A23DE2B516CBB;1683.
LaTeX Warning: There were multiply-defined labels.
Package atveryend Info: Empty hook `AtVeryVeryEnd' on input line 342.
Package atveryend Info: Empty hook `AtVeryVeryEnd' on input line 415.
)
Here is how much of TeX's memory you used:
12809 strings out of 481239
188860 string characters out of 5920377
494798 words of memory out of 5000000
27720 multiletter control sequences out of 15000+600000
12829 strings out of 481239
189098 string characters out of 5920377
495801 words of memory out of 5000000
27729 multiletter control sequences out of 15000+600000
594958 words of font info for 74 fonts, out of 8000000 for 9000
1141 hyphenation exceptions out of 8191
39i,9n,45p,1077b,426s stack positions out of 5000i,500n,10000p,200000b,80000s
39i,14n,45p,1077b,475s stack positions out of 5000i,500n,10000p,200000b,80000s
{/usr/share/texmf/fonts/enc/dvips/lm/lm-rm.enc}{/usr/share/texmf/fonts/enc/dv
ips/lm/lm-mathex.enc}{/usr/share/texmf/fonts/enc/dvips/lm/lm-mathit.enc}{/usr/s
hare/texmf/fonts/enc/dvips/lm/lm-mathsy.enc}{/usr/share/texmf/fonts/enc/dvips/l
......@@ -1123,10 +1165,10 @@ lm/lmr17.pfb></usr/share/texmf/fonts/type1/public/lm/lmr6.pfb></usr/share/texmf
b></usr/share/texmf/fonts/type1/public/lm/lmro17.pfb></usr/share/texmf/fonts/ty
pe1/public/lm/lmsy10.pfb></usr/share/texmf/fonts/type1/public/lm/lmsy6.pfb></us
r/share/texlive/texmf-dist/fonts/type1/public/amsfonts/symbols/msam10.pfb>
Output written on compte_rendu_zg2.pdf (12 pages, 13516431 bytes).
Output written on compte_rendu_zg2.pdf (13 pages, 13525701 bytes).
PDF statistics:
314 PDF objects out of 1000 (max. 8388607)
234 compressed objects within 3 object streams
52 named destinations out of 1000 (max. 500000)
246 words of extra memory for PDF output out of 10000 (max. 10000000)
356 PDF objects out of 1000 (max. 8388607)
275 compressed objects within 3 object streams
63 named destinations out of 1000 (max. 500000)
294 words of extra memory for PDF output out of 10000 (max. 10000000)
......@@ -10,6 +10,12 @@
\BOOKMARK [3][-]{subsubsection.3.1.2}{Bilan et confrontation des r\351sultats}{subsection.3.1}% 10
\BOOKMARK [2][-]{subsection.3.2}{Semaines 2 et 3}{section.3}% 11
\BOOKMARK [3][-]{subsubsection.3.2.1}{Temps 1}{subsection.3.2}% 12
\BOOKMARK [1][-]{section.4}{Partie Math\351matiques}{}% 13
\BOOKMARK [2][-]{subsection.4.1}{Semaine 1}{section.4}% 14
\BOOKMARK [3][-]{subsubsection.4.1.1}{Pourquoi les syst\350mes vus en ZG \351taient descriptibles par des \351quations diff\351rentielles ?}{subsection.4.1}% 15
\BOOKMARK [3][-]{subsubsection.3.2.2}{Temps 2}{subsection.3.2}% 13
\BOOKMARK [1][-]{section.4}{Partie Math\351matiques}{}% 14
\BOOKMARK [2][-]{subsection.4.1}{Semaine 1}{section.4}% 15
\BOOKMARK [3][-]{subsubsection.4.1.1}{Pourquoi les syst\350mes vus en ZG \351taient descriptibles par des \351quations diff\351rentielles ?}{subsection.4.1}% 16
\BOOKMARK [1][-]{section.5}{R\351solution num\351rique}{}% 17
\BOOKMARK [1][-]{section.6}{Synth\350se}{}% 18
\BOOKMARK [2][-]{subsection.6.1}{Similarit\351s th\351orique \(calcul\351es lor de la premi\350re activit\351\)}{section.6}% 19
\BOOKMARK [2][-]{subsection.6.2}{Similarit\351s lors de l\220exp\351rimentation}{section.6}% 20
\BOOKMARK [1][-]{section.7}{Bibliographie}{}% 21
......@@ -314,6 +314,33 @@ $$U_c(t) = U_{\infty} + (U_c(t_0) - U_{\infty}) e^{\frac{-(t-t_0)}{\tau}} $$
Nous pouvons ainsi déterminer la période $T_A$:
$$\frac{5}{3} = 5 + (\frac{5}{3} - 5) e^{\frac{-T_A}{(R_A + R_B)C}}$$
$$T_A = ln(2)(R_A + R_B)C$$
\subsubsection{Temps 2}
\paragraph{Activité 1}\mbox{}\\
Explication des lignes de codes présentes dans le programme pour faire fonctionner le capteur:\\
\begin{table}[H]
\centering
\scalebox{0.9}{
\begin{tabular}{|l|l|}
\hline
\multicolumn{1}{|c|}{\textbf{Ligne de Code}} & \multicolumn{1}{c|}{\textbf{Explication}} \\ \hline
const uint8\_t sensorPin = 2; & “applique une constante au Pin 2” / on utilise le pin 2 comme sensorPin \\ \hline
Serial.begin(115200); & “vitesse de transmission et de réception de données = 115200” \\ \hline
int16\_t t = pulseIn(sensorPin, HIGH); & “t = temps de l’état haut du signal” \\ \hline
int16\_t d = (t - 1000) * 2; & “d = différence de temps de l’état au du signal” \\ \hline
Serial.print("S"); & “affiche S” \\ \hline
delay(10); & “temps de délai à la fin de la boucle” \\ \hline
\end{tabular}}
\end{table}
\paragraph{Activité 3}\mbox{}\\
$$R = 470 \Omega$$
$$Tension = 5V$$
\paragraph{Activité 4}\mbox{}\\
L'intervalle de temps entre 2 mesures n’est pas toujours la même. En effet, le "void loop()" ne s’exécute pas à la même vitesse suivant l’action à effectuer ( en fonction de la position du mobile.) La ligne //delay(10); fait attendre que l’action a effectuer soit terminée avant de recommencer. \\
Il est nécessaire ainsi de réaliser une une interruption afin d’uniformiser les temps.
\section{Partie Mathématiques}
\subsection{Semaine 1}
......@@ -336,7 +363,53 @@ Dans le système électrique, le circuit est composé d’une inductance et d’
\includegraphics[scale=0.3]{images/cr1/rlc.png}
\end{figure}
\begin{itemize}
\item A partir du schéma du circuit RLC série, on énonce les relations tension-courant aux bornes de chaque composant:
$$U_R = R \times I$$
$$U_L = L \frac{dI}{dt}$$
$$I = \frac{dU_c}{dt}$$
On trouve l’équation différentielle de l’expression de la tension Uc grâce à la loi des mailles:
$$U_R + U_L + U_C = 0$$
$$RC \frac{dU_c}{dt} + L \frac{dI}{dt} + U_C = 0$$
$$\frac{1}{LC} U_C + \frac{R}{L} \frac{dU_c}{dt} + \frac{d^2 U_C}{dt^2} = 0$$
\item On obtient 2 équations différentielles du deuxième ordre à coefficient directeur = 1,
on peut donc faire correspondre les équations par analogie dans le tableau suivant:
\begin{figure}[H]
\begin{table}[H]
\centering
\scalebox{1.2}{
\begin{tabular}{|ll|ll|}
\hline
\multicolumn{2}{|l|}{Grandeurs mécaniques} & \multicolumn{2}{l|}{Grandeurs électriques} \\ \hline
\multicolumn{1}{|l|}{Force} & F & \multicolumn{1}{l|}{$U = 0$} & Tension d'entrée \\ \hline
\multicolumn{1}{|l|}{Position} & x & \multicolumn{1}{l|}{q} & Charge en Coulomb \\ \hline
\multicolumn{1}{|l|}{Frottements} & a & \multicolumn{1}{l|}{R} & Résistance \\ \hline
\multicolumn{1}{|l|}{Masse} & m & \multicolumn{1}{l|}{L} & Inductance \\ \hline
\multicolumn{1}{|l|}{Raideur} & k & \multicolumn{1}{l|}{$\frac{1}{C}$} & Inverse de la Capacité \\ \hline
\end{tabular}}
\end{table}
\caption{Tableau d'analogie Mécanique/Électrique}
\end{figure}
\end{itemize}
\section{Résolution numérique}
\section{Synthèse}
\subsection{Similarités théorique (calculées lor de la première activité)}
Nous avons observé des similarités entre le système mécanique masse-ressort et le circuit électrique RLC. \\
Dans l’équation différentielle, on peut associer la position x du point d’attache de l’amortisseur à la charge q d’un condensateur dans un circuit RLC. On peut également associer la force F à la tension d’entrée U, les frottements a à la résistance R, la masse m à l’inductance L et la raideur k à l’inverse de la capacité.\\
On peut donc associer les équations différentielles suivantes : \\
$$F = \frac{d^2 x}{dt^2} + \frac{a}{m} \frac{dx}{dt} + \frac{k}{m} x$$
$$\frac{1}{LC} U_C + \frac{R}{L} \frac{dU_c}{dt} + \frac{d^2 U_C}{dt^2} = 0$$
\subsection{Similarités lors de l’expérimentation}
On observe des résultats de forme similaire au niveau des courbes et des signaux obtenus. Ils sont de forme périodique, apériodique, critique ou pseudo-périodique.
\section{Bibliographie}
polycopié dynamique\\
bibliothèque matplotlib pour tracer des graphs\\
stackoverflow\\
\end{document}
\ No newline at end of file
......@@ -15,6 +15,15 @@
\contentsline {subsubsection}{\numberline {3.2.1}Temps 1}{8}{subsubsection.3.2.1}%
\contentsline {paragraph}{Caractérisation du signal Vdistance(t):}{8}{section*.5}%
\contentsline {paragraph}{Le 555 Astable}{9}{section*.6}%
\contentsline {section}{\numberline {4}Partie Mathématiques}{10}{section.4}%
\contentsline {subsection}{\numberline {4.1}Semaine 1}{10}{subsection.4.1}%
\contentsline {subsubsection}{\numberline {4.1.1}Pourquoi les systèmes vus en ZG étaient descriptibles par des équations différentielles ?}{10}{subsubsection.4.1.1}%
\contentsline {subsubsection}{\numberline {3.2.2}Temps 2}{10}{subsubsection.3.2.2}%
\contentsline {paragraph}{Activité 1}{10}{section*.7}%
\contentsline {paragraph}{Activité 3}{10}{section*.8}%
\contentsline {paragraph}{Activité 4}{10}{section*.9}%
\contentsline {section}{\numberline {4}Partie Mathématiques}{11}{section.4}%
\contentsline {subsection}{\numberline {4.1}Semaine 1}{11}{subsection.4.1}%
\contentsline {subsubsection}{\numberline {4.1.1}Pourquoi les systèmes vus en ZG étaient descriptibles par des équations différentielles ?}{11}{subsubsection.4.1.1}%
\contentsline {section}{\numberline {5}Résolution numérique}{12}{section.5}%
\contentsline {section}{\numberline {6}Synthèse}{12}{section.6}%
\contentsline {subsection}{\numberline {6.1}Similarités théorique (calculées lor de la première activité)}{12}{subsection.6.1}%
\contentsline {subsection}{\numberline {6.2}Similarités lors de l’expérimentation}{12}{subsection.6.2}%
\contentsline {section}{\numberline {7}Bibliographie}{12}{section.7}%
Supports Markdown
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment