Avancées

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Feror 2025-09-30 15:51:58 +02:00
parent 67bb137fe1
commit e8a06b1520
44 changed files with 1959 additions and 4 deletions

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![[2.1_cours_AFexterne_2025_1A.pdf]]
Bête à cornes, Diag. Pieuvre et Matrice de confomité.

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@ -133,3 +133,6 @@ Chaque phase du cycle apporte des contraintes supplémentaires, il faut les pré
- Éco-concepteur : intègre les critères environnementaux dès la phase de conception. - Éco-concepteur : intègre les critères environnementaux dès la phase de conception.
- Concepteur en énergies renouvelables : imagine des systèmes solaires, éoliens ou hydrauliques adaptés aux besoins. - Concepteur en énergies renouvelables : imagine des systèmes solaires, éoliens ou hydrauliques adaptés aux besoins.
- Urbaniste / concepteur despaces publics : développe des aménagements durables pour les villes. - Urbaniste / concepteur despaces publics : développe des aménagements durables pour les villes.

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---
excalidraw-plugin: parsed
tags: [excalidraw]
---
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
# Excalidraw Data
## Text Elements
Produit ^loypJHar
Utilisateur d'une table élévatrice ^tLkViNto
Position de l'utilisateur ^CH5fkQAD
Permettre à l'utilisateur d'une table élévatrice d'être en position assis et assis-debout. ^caSxgSOI
%%
## Drawing
```compressed-json
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```
%%

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@ -0,0 +1,209 @@
---
excalidraw-plugin: parsed
tags: [excalidraw]
---
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
# Excalidraw Data
## Text Elements
AquaBoost ^lLZKnkBr
Soleil ^XKiv3e3E
Utilisateur ^hHXHdIzg
Eau de pluie ^mv3NhWsh
Phase: Utilisation ^q07ZLmeJ
Air ambiant / Environnement ext. ^tO1joEs7
Espace d'installation
(Balcon/Rambarde/Terrasse) ^cqeDgz4X
Smartphone ^ysHVezus
Réseau eau domestique non potable ^ogH7GA0U
Wifi ^DUFbuws2
Normes sanitaires ^GzhSkfGK
Plantes ^41O3KoeO
FP1 ^4QMlgEGQ
FC1 ^D6cSlZ6I
FC2 ^jp7v4wzX
FC3 ^TM5CmkpE
FC4 ^ZiwCCBNV
FC5 ^gL7SjtVk
FC6 ^QD8k8fDp
FC7 ^Dx4UKjJr
FC8 ^z0x0Y5gn
FC9 ^JYSKnZCj
FC10 ^JZtz3Fc5
FC11 ^J6ybsiN8
FC12 ^s9AlkNjB
%%
## Drawing
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```
%%

View file

@ -0,0 +1,70 @@
---
excalidraw-plugin: parsed
tags: [excalidraw]
---
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
# Excalidraw Data
## Text Elements
AquaBoost ^0tTqdbKd
Particulier vivant en appartement ou petite maison sans jardin ^O4tFV7ve
L'eau de pluie ^ebHnCe1V
Récupérer, filtrer, stocker et réutiliser l'eau de pluie à domicile. ^UqWfulFK
%%
## Drawing
```compressed-json
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```
%%

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# Diag. Pieuvre
Un truc au centre, avec des éléments internes et externes. Il est dans un milieu et les éléments qui l'entourent sont concrets.
Une FP (Fonction Principale) relie 2 ou plus éléments au système
Une FC (Fonction Contrainte) relie 1 élément au système.
# Les « horreurs » dinternet
## 1.
![[Pasted image 20250926090602.png]]
Pas de phase de cycle de vie. ($\Phi =$ Utilisation)
FC6 ne parait pas cohérent (relié à "utilisateur" alors que faisant référence à "Ambiance extérieure")
Ambiance extérieure c'est quoi ???
FP1 $+=$ "à partir d'énergie électrique"
FC3 devrait relier le produit à Utilisateur
FC5 n'a rien à faire dans une analyse fonctionnelle.
## 2.
![[Pasted image 20250926091223.png]]
Pas de phase de cycle de vie.
Moteur, Puce, Pince pas externes.
Esthétique et FC6 n'ont rien à faire dans une analyse fonctionnelle.
Solidité n'est pas concret ou tangible.
Sécurité n'est pas concret ou tangible.
## 3.
![[Pasted image 20250926092043.png]]
Pas de cycle de vie.
Doseur intern au produit
Information et écologique pas concrets.
```ad-warning
Réglementation toujours concret.
```
Si on peut contourner les normes et la réglementation, c'est mieux (frauder c'est bien).
# Pratique
## 1.
![[Pasted image 20250926093440.png]]
![[ChaiseElevatrice]]
Solution:
![[Pasted image 20250926094537.png]]
| Fonction | Nom |
| -------- | -------------------------------------------------------------------- |
| FP1 | Permettre à l'utilisateur de s'assoir à hauteur de la table. |
| FP2 | Permettre à l'utilisateur de se rapprocher de la table. |
| FC1 | Permettre la rotation de l'utilisateur. |
| FC2 | Resister aux balancements de l'utilisateur. |
| FC3 | Permettre de micro-ajustements de hauteur par rapport à la table. |
| FC4 | Être contrôlable (accès aux commandes) |
| FC5 | Permettre aux mains (ou coudes) des appuis pour le repositionnement. |
| FC6 | Maintenir le dos de l'utilisateur. |
| FC7 | Être mobile sous charge. |
| FC8 | Resister à la charge de l'utilisateur. |
| | |
## 2.
![[Pasted image 20250926100241.png]]
![[Pasted image 20250926100312.png]]
![[Pasted image 20250926100347.png]]
Bête à cornes: ![[SystèmeDeFlote]]
Diagramme pieuvre:
![[DiagrammePieuvreSystèmeFlotte|1000]]
| Fonction | Nom |
| -------- | ---------------------------------------------------------------------------------------------------------- |
| FP1 | Permettre à l'utilisateur d'utiliser l'eau de pluie pour alimenter le réseau en eau domestique non potable |
| FC1 | Être connecté à internet |
| FC2 | S'Alimenter via le soleil |
| FC3 | Respecter les normes sanitaires |
| FC4 | Communiquer les infos avec le smartphone |
| FC5 | Être adapté à l'espace d'installation |
| FC6 | Récolter l'eau de pluie |
| FC7 | Arroser les plantes |
| FC8 | Resister à l'environnement. |
| FC9 | Facile à installer |
| FC10 | Stocker l'eau de pluie |
| FC11 | Refouler le trop plein |
| FC12 | Être compatible avec le réseau domestique. |
Matrice de conformité:
| Fonction | Critère d'appreciation | Niveau | Flexibilité |
| --------------------------------------------------------------------------- | ---------------------- | ------ | ----------- |
| FP1: Permettre à l'usager d'acheminer l'eau de pluie vers un point d'usage. | Débit en entrée | 5L/min | |
| ^ | Débit en sortie | 2L/min | |
| ^ | Volume d'eau stocké | 30L | |

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@ -0,0 +1,152 @@
---
excalidraw-plugin: parsed
tags: [excalidraw]
---
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
# Excalidraw Data
## Text Elements
AquaBoost ^RSfE5MwD
Récolter et filtrer l'eau de pluie ^tXoe3CYX
A0 ^XMD6isF6
Eau de pluie ^hAUCpv0g
Niveau de trop plein ^veTub7pI
Eau non potable pour le réseau domestique ^PYbjwqCh
Débit d'entrée ^VJxRu9Q0
Débit de sortie ^dib1MOgr
Eau rejetée ^8x4VsbRU
%%
## Drawing
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```
%%

View file

@ -0,0 +1,304 @@
---
excalidraw-plugin: parsed
tags: [excalidraw]
---
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
# Excalidraw Data
## Text Elements
Préparer le café ^aAAQnBC3
A0 ^bj3wp8YP
Cafetière électrique ^8AhDSQdm
W: Électricité ^Kp1SMJmm
Café moulu ^CObDUQtH
Café liquide chaud ^DRpM2rgV
Eau froide ^bKH6s6fS
E: Bouton marche arrêt ^bkaibLL9
A0 ^93I4CbhR
Filtre ^sI5vYF8e
Filtre + Moût ^86eBWPtq
Chauffer l'eau ^HkRyVw8D
Eau froide ^XN6ExLR4
Eau chaude ^2lpEsyZ5
Maintenir le filtre ^I1F1ftMA
Contenir le café ^whTpyI9n
Maintenir la température ^4191pvD6
Café moulu ^CGYZQdsZ
Filtre ^uW8igYhu
Filtre + Moût ^oTc0NwJd
A1 ^uf5blcu7
A2 ^oFsv67s4
A3 ^IJYdDmht
A4 ^sVKhTvXm
W: Électricité ^UBD62U90
E: Bouton marche arrêt ^GAxpngWl
Café liquide chaud ^YXqUDXR9
Résistance ^9ORqxLL7
Support ABS ^drufZXFd
Carafe ^hfQ17LSy
Résistance ^gn8HcFaQ
%%
## Drawing
```compressed-json
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```
%%

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@ -0,0 +1,8 @@
![[3.2_RAPPELcours_AFinterne_2024_1A_moodle.pdf]]
Ex.
# La machine à café.
![[Café|1000]]
# Aquaboost
![[Aquaboost|1000]]

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@ -14,7 +14,8 @@ Car: Tiny blue car.
Dream car: Ford Mustang (from the 60s) Dream car: Ford Mustang (from the 60s)
# IELTS: Writing Task 1 - Visual Information # IELTS
## Writing Task 1 - Visual Information
This bar chart shows the percentage of the population living in urban areas, worldwide and on specific continents, from 1950 to 2030. This bar chart shows the percentage of the population living in urban areas, worldwide and on specific continents, from 1950 to 2030.
Overall, the percentage has only been rising from 1950 to 2030, with the most urbanized continent being North America followed by Latin America. Worldwide, the percentage has doubled. Overall, the percentage has only been rising from 1950 to 2030, with the most urbanized continent being North America followed by Latin America. Worldwide, the percentage has doubled.
@ -27,3 +28,30 @@ Teacher's input:
- Make it even clearer - Make it even clearer
## Writing Task 2 - Essay
You should spend about 40 minutes on this task.
Write about the following topic:
Some people think that the increase in international travel has a negative
impact on the environment and should be restricted.
To what extent do you agree or disagree with this opinion?
Give reasons for your answer and include any relevant examples from your own
knowledge or experience.
Write at least 250 words.
Plan:
- Intro (speak about the topic of environment and international travel)
- Paragraph 1: Why it is undeniable that international travel has a negative impact on the environment
- Paragraph 2: Why it shouldn't mandate a travel ban
- Conclusion
Our environment is fragile and its protection is without a doubt the most important discussion of the century. The topic of climate change has grown in the past few decades, but so has international traveling. While I agree with the analysis that international travel has a negative impact on the environment, I do not think that restricting said travel will have a positive impact.
All means of transportation have an impact on the environment. The vector of that impact can vary (carbon footprint, pollution, etc...), and the magnitude of it may too, but as careful as one can be, there is no such thing as a 100% clean travel. International travel implies long distances, most of the time using airplanes (which are very high carbon intensity). It is undeniable that international travel is responsible for some amount of damage done to the environment.
However, I would argue that applying a restriction to international travel would be both unfeasible and ineffective. It would be unfeasible firstly because it would be unconstitutional in most countries to restrict the movements of their citizens in and out of the territory (not even taking into account the riots such a policy would cause). I also think it would be ineffective to restrict international travel because the domestic transportation environmental impact simply overshadows that of international travel. Taylor Swift alone has the carbon footprint of a small country.
Overall, I would say that denying the impact of transportation would be disingenuous. I do however wholeheartedly believe that restricting international travel would not yield the results people might expect.

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@ -62,6 +62,17 @@ b --> bb((" "))
``` ```
En parallèle, c'est la somme des inverses ($R_{parallèle}=\sum{\frac{1}{R_i}}$) En parallèle, c'est la somme des inverses ($R_{parallèle}=\sum{\frac{1}{R_i}}$)
2 Resistances identiques en parallèle ont pour somme la moitié.
Ex:
```mermaid
flowchart LR
aa((" ")) --> a
a((" ")) --> R1["2R"] --> b((" "))
a((" ")) --> R2["2R"] --> b((" "))
b --> bb((" "))
```
$R_{eq}=R$
Le condensateur est un composant. Généralement deux surfaces conductrices séparées d'un isolant. Ça retarde la transmission. Le condensateur est un composant. Généralement deux surfaces conductrices séparées d'un isolant. Ça retarde la transmission.
Calculer la somme -> Inverse de la résistance Calculer la somme -> Inverse de la résistance
@ -81,7 +92,20 @@ Lois Kirchhoff:
### 3. Circuits en régime permanent ### 3. Circuits en régime permanent
Le diviseur de tension est un montage électronique simple qui permet de diviser une tension d'entrée. Le diviseur de tension est un montage électronique simple qui permet de diviser une tension d'entrée.
![[Pasted image 20250924160957.png]] $\implies \boxed{V_1=\frac{R_1}{R_1+R_2}V}$
Le diviseur de courant est un montage simple permettant d'obtenir un courant proportionnel à un autre courant. Le diviseur de courant est un montage simple permettant d'obtenir un courant proportionnel à un autre courant.
![[Pasted image 20250924161028.png]]$\implies \boxed{i_1=\frac{R_2}{R_1+R_2}i}$
Le théorème de superposition. Le théorème de superposition.
Les circuits sont linéaires, donc si j'ai plusieurs générateurs, je peux étudier le circuit un générateur à la fois et additionner le tout. Les circuits sont linéaires, donc si j'ai plusieurs générateurs, je peux étudier le circuit un générateur à la fois et additionner le tout.
Théorème de Thevenin:
N'importe quel circuit peut être résumé en un générateur de tension avec une résistance en série.
Théorème de Norton:
N'importe quel circuit peut être résumé en un générateur de courant avec une résistance en parallèlle.
$R_{Th}=R_{N}$
Théorème de Millman
-> Le théorème bulldozer

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@ -65,3 +65,32 @@ $$
$E_2=\frac{E_1R_3}{R_1+R_3}+i_2(R_2+R_3-\frac{R_3^2}{R_1+R_3})$ $E_2=\frac{E_1R_3}{R_1+R_3}+i_2(R_2+R_3-\frac{R_3^2}{R_1+R_3})$
$\implies i_2=(E_2-\frac{E_1R_3}{R_1+R_3})\times \frac{R_1+R_3}{R_2(R_1+R_3)+R_3(R_1+R_3)-R_3^2}$ $\implies i_2=(E_2-\frac{E_1R_3}{R_1+R_3})\times \frac{R_1+R_3}{R_2(R_1+R_3)+R_3(R_1+R_3)-R_3^2}$
$i_2=\frac{E_2(R_1R_3)-E_1R_3}{R_1R_2+R_1R_3+R_2R_3}$ $i_2=\frac{E_2(R_1R_3)-E_1R_3}{R_1R_2+R_1R_3+R_2R_3}$
# Exercise 3.
1. $V=V_1+V_2$
$V=R_1i+R_2i$
$i=V\times\frac{1}{R_1+R_2}\implies V_1=\frac{V\times R_1}{R_1+R_2}$
2. $V_1=\frac{V\times R_1}{R_1+(R_2+R_3)}$
3. $\frac{1}{R_{eq}}=\frac{1}{R_2}+\frac{1}{R_3}$
$R_{eq}=\frac{R_2R_3}{R_2+R_3}$
$V_3=\frac{R_{eq}}{R_1+R_{eq}}V$
# Exercise 4.
1. $i=i_1+i_2\implies i=V(\frac{1}{R_1}+\frac{1}{R_2})\implies V=i\times\frac{R_1R_2}{R_1+R_2}$
$i_1=\frac{V}{R_1}=i\frac{R_1R_2}{R_1+R_2}\times\frac{1}{R_1}$
$i_1=\frac{R_2}{R_1+R_2}i$
2. $i_1=\frac{R_{eq}}{R_1+R_{eq}}i$
$R_{eq}=\frac{R_2R_3}{R_2+R_3}$
$i_1=\frac{\frac{R_2R_3}{R_2+R_3}}{R_1+\frac{R_2R_3}{R_2+R_3}}i$
3. $i_3=\frac{R_2}{R_2+R_3}$
# Exercice 5
![[Pasted image 20250924163225.png]]
![[Pasted image 20250924163232.png]]
$i_2a=\frac{E_2}{R_{eq}}$
$R_{eq}=4R$
$i_2a=\frac{E_2}{4R}$
Par diviseur de courant, $i_1a=\frac{-2R}{2R+2R}i_2a$
![[Pasted image 20250924163239.png]]

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![[TD_FGE_2025.pdf]]

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---
excalidraw-plugin: parsed
tags: [excalidraw]
---
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
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%%
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```
%%

View file

@ -0,0 +1,145 @@
---
excalidraw-plugin: parsed
tags: [excalidraw]
---
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
# Excalidraw Data
## Text Elements
y ^3QxVlAAV
x ^imj90nWK
A ^MCKdM432
B ^6B1Sz5ch
O ^aU96UPNR
l ^xYgftC0t
Ɵ₂ ^3xSbfyyh
b ^Sn3e4r85
r ^KMRosYXL
Ɵ₁ ^nlhN4qnW
x ^BiXkYr83
Ɵ₁ ^6x1cIlGr
## Embedded Files
fa685800f92b0207abbf06437697e5a36c828afe: $$\color{green}\alpha_2$$
d5a12c14bef44f37f874559a91d5513f3194d72c: $$\color{green}\alpha_1$$
%%
## Drawing
```compressed-json
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```
%%

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@ -0,0 +1,105 @@
Un solide est un ensemble de points qui veut être en translation, en rotation...
Notions:
- Produits vectoriels/scalaires
- Matrice d'inertie
Matrice d'inertie: Permet de définir l'énergie demandée pour appliquer une rotation à un solide (ou sa resistance à la rotation).
Inertie est au moment ce que la force est à la translation.
```python
import micropip
await micropip.install('matplotlib')
await micropip.install('numpy')
import matplotlib.pyplot as plt
import numpy as np
# Plot in 3D
fig = plt.figure()
fig.set_label('3D plot')
ax = fig.add_subplot(111, projection='3d')
# Plot the vectors
ax.quiver(0, 0, 0, 5, 5, 5, color='r')
ax.quiver(5, 5, 5, 2, 2, -2, color='b')
ax.quiver(7, 7, 3, 2, 2, 6, color='g')
# Add vector names
ax.text(5, 5, 5, 'A', color='r')
ax.text(7, 7, 3, 'B', color='b')
ax.text(9, 9, 9, 'M', color='g')
# Set the aspect of the plot to be equal
ax.set_box_aspect([10,10,10])
size = 10
ax.set_xlim([0, size])
ax.set_ylim([0, size])
ax.set_zlim([0, size])
plt.show()
```
![[Drawing 2025-09-25 11.16.23.excalidraw|1000]]
À gauche, $\theta_1$ est positif, et à droite $\theta_1$ est négatif.
Soit $\alpha_1$ l'angle entre l'axe $\overrightarrow{x}$ et $\overrightarrow{OA}$
$\alpha_1=\theta_1+\frac{\pi}{2}$
$\overrightarrow{OA}=l_1(\cos{\alpha_1}\overrightarrow{x}+\sin{\alpha_1}\overrightarrow{y})$
$\overrightarrow{OA}=l_1(\cos{(\theta_1+\frac{\pi}{2})}\overrightarrow{x}+\sin{(\theta_1+\frac{\pi}{2})}\overrightarrow{y})$
Or, par cercle trigonométrique, $\cos{(\theta_1+\frac{\pi}{2})}=-\sin{\theta_1}$ et $\sin{(\theta_1+\frac{\pi}{2})}=\cos{\theta_1}$
Donc $\overrightarrow{OA} = l_1(-\sin{\theta_1}\overrightarrow{x}+\cos{\theta_1}\overrightarrow{y})$
$\sin{\alpha}=\frac{AB}{OB}\implies OB=\frac{AB}{\sin{\alpha}}$
$\alpha_2=\alpha_1+\pi+\theta_2$
$\alpha_2=\theta_1+\frac{\pi}{2}+\pi+\theta_2$
$\alpha_2=\theta_1+\theta_2+\frac{3\pi}{2}$
$\overrightarrow{AB}=l_2(\cos{\alpha2}\overrightarrow{x}+\sin{\alpha2}\overrightarrow{y})$
Avec $\alpha_2=\theta_1+\theta_2+\frac{3\pi}{2}$
Soit $\alpha_{1+2}=\theta_1+\theta_2$
$\cos{(\alpha_{1+2}+\frac{3\pi}{2})}=\sin{\alpha_{1+2}}$
$\sin{(\alpha_{1+2}+\frac{3\pi}{2})}=-\cos{\alpha_{1+2}}$
Donc $\overrightarrow{AB}=l_2(\sin{(\theta_1+\theta_2)}\overrightarrow{x}-\cos{(\theta_1+\theta_2)}\overrightarrow{y})$
# Exo2
![[Drawing 2025-09-25 12.21.28.excalidraw]]
$\overrightarrow{OA}=r(\cos{\theta_1}\overrightarrow{x}+\sin{\theta_1}\overrightarrow{y})$
$\alpha_2=\theta_1+\pi+\theta_2$
$\overrightarrow{AB}=b(\cos{\alpha_2}\overrightarrow{x}+\sin{\alpha_2}\overrightarrow{y}) = b(-\cos{(\theta_1+\theta_2)}\overrightarrow{x}-\sin{(\theta_1+\theta_2)}\overrightarrow{y})$
![[MG.pdf#page=11]]
# Cinématique
$\overrightarrow{V}_{M\in S_s/R_0}=\frac{d}{dt}\overrightarrow{O_0M}(t)|_{B_0}$
![[TD-Ven. 26 septembre 2025|1000]]
Par relation de Chales,
$\overrightarrow{O_0A}=\overrightarrow{O_0I}+\overrightarrow{IO_1}+\overrightarrow{O_1A}$
$= X(t)\overrightarrow{x_0} + R\overrightarrow{y_0}+R\overrightarrow{x_1}$
$\overrightarrow{V}_{A\in{1/0}}=\frac{d}{dt}\overrightarrow{O_0A}|_0$
--> le $0$ dans $1/0$ correspond à $(O_0,B_0)$ avec $O_0$ l'origine et $B_0$ la base.
$\frac{d\overrightarrow{IO_1}}{dt}|_0=\frac{d}{dt}R\overrightarrow{y_0}|_0=\frac{d}{dt}R|_0\overrightarrow{y_0}+R\frac{d\overrightarrow{y_0}}{dt}|_0$
![[TD-Ven. 26 septembre 2025 - 2]]
$\frac{d\overrightarrow{x_1}}{dt}|_0=?$
$\overrightarrow{x_1}=||\overrightarrow{x_1}||(\cos{\theta}\overrightarrow{x_0}+\sin{\theta}\overrightarrow{y_0})$
$\frac{d\overrightarrow{x_1}}{dt}|_0=(\frac{d}{dt}\cos{\theta(t)})\overrightarrow{x_0}+\cos{theta}\frac{d\overrightarrow{x_0}}{dt}|_0+\frac{d}{dt}(\sin{\theta(t)})\overrightarrow{y_0}+\sin{\theta}\frac{d\overrightarrow{y_0}}{dt}$
$= -\dot{\theta}\sin{\theta}\overrightarrow{x_0}+\dot{\theta}\cos{\theta}\overrightarrow{y_0}$
$\Omega_{1/0}=\dot{\theta} \overrightarrow{z}$
$xyzxyz$
Pour calculer le produit vectoriel de $x$ et $y$, on prend le suivant ($z$)
Vers la droite, c'est positif ($x • y = z$) et vers la gauche c'est négatif ($y • x = -z$)

BIN
ModélisationEnMeca/MG.pdf Normal file

Binary file not shown.

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---
excalidraw-plugin: parsed
tags: [excalidraw]
---
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
# Excalidraw Data
## Text Elements
## Embedded Files
c8bc2bb1cbb61f91ae8ec7f4acafdab195a9fbae: $$0_0$$
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a2c0bd07022c6a2b67419fabac13c3e99fe250f8: $$\overrightarrow{x_1}$$
a29c076d33bc126c42f62ff7748993b1a26e026e: $$\theta$$
%%
## Drawing
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```
%%

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@ -0,0 +1,119 @@
---
excalidraw-plugin: parsed
tags: [excalidraw]
---
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
# Excalidraw Data
## Text Elements
I ^ib0tGhJj
A ^haMPIGgH
X(t) ^jaSTI6Dc
## Embedded Files
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%%
## Drawing
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```
%%

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# Ch1 - Introduction
Signal analogique: Signal qui varie de façon continue dans le temps.
Classification de signaux:
```mermaid
flowchart LR
Signal --> Analogique
Signal --> Numérique
Analogique --> Continu
Analogique --> Temporel
Analogique --> Fréquentiel
Numérique --> TOR
Numérique --> t["Train d'implusion"]
Numérique --> Échantillonage
```
# Ch2 - L'Amplificateur Opérationnel (AOP) en régime linéaire
Le principe: Amplifier.
L'amplification s'exprime en dB ou en linéaire.
AOP Idéal: ![[Pasted image 20250929162848.png]]
$i^+=i^-=0$, $Z_e\rightarrow∞$ , $\Delta f \rightarrow ∞$
L'amplification est considérée infinie: $A_0\rightarrow ∞$
Régime linéaire: Contre réaction sur la borne $\boxed{-}$ $\implies v^+=v^-$
$V^-=\frac{\frac{V_s}{R_1}}{\frac{1}{R_1}+\frac{1}{R_2}}$
$=\frac{V_S}{\frac{R_2+R_1}{R_2}}=\frac{R_2V_S}{R_1+R_2}$
$V_S=R_1I+R_2I=I(R_1+R_2)\implies I=\frac{VS}{R_1+R_2}$
$V^-=R_2I=\boxed{\frac{R_2V_S}{R_1+R_2}}$
Millman en $y$:
![[millmanEnY]]
$V_y=\frac{\frac{V_A}{R_A}+\frac{V_B}{R_B}+\frac{V_C}{R_C}}{\frac{1}{R_A}+\frac{1}{R_B}+\frac{1}{RC}}$

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---
excalidraw-plugin: parsed
tags: [excalidraw]
---
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
# Excalidraw Data
## Text Elements
I ^yvOkwrhc
i- ^fqmKrEsI
v- ^Jd87KXuV
Vs ^YJYjfaou
R1 ^SwgTHZyd
R2 ^snNR5WC5
%%
## Drawing
```compressed-json
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```
%%

View file

@ -0,0 +1,74 @@
---
excalidraw-plugin: parsed
tags: [excalidraw]
---
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
# Excalidraw Data
## Text Elements
Ve ^e5e5GfnX
Vs ^AzPulmGg
R1 ^5EQzmgKB
R2 ^QTeYMkUn
V- ^0GZmKqcJ
%%
## Drawing
```compressed-json
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```
%%

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Électronique/TD1/TD1.md Normal file
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# Exercice ARL2.
## 2.1
1. ![[Drawing 2025-09-29 17.00.30.excalidraw|100]]
$V^-=\frac{v_s}{\frac{R_2+R_1}{R_2}}\implies V^-=\frac{R_2v_s}{R_1+R_2}$
2. CR sur $\boxed{-}$, donc $V^+=V^-$ d'ou $V^-=V_e$
3. On a $V^-=\frac{R_2v_s}{R_1+R_2}=V_e$
D'ou $\frac{R_2}{R_1+R_2}=\frac{V_e}{V_s}=\frac{R_1+R_2}{R_2}=1+\frac{R_1}{R_2}$
4. Avec $R_1=3K\Omega$ et $R_2=9K\Omega$
$\frac{V_s}{V_e}=\frac{4}{3}$
## 2.2
1. ![[Drawing 2025-09-29 17.15.52.excalidraw]]
En appliquant le théorème de Millman au point $V^-$,
$\boxed{V^-=\frac{\frac{V_e}{R_1}+\frac{V_s}{R_2}}{\frac{1}{R_1}+\frac{1}{R_2}}}$
2. Dans un régime linéaire (On sait qu'on est en régime linéaire car la sortie du triangle est reliée à l'entrée - du triangle), $V^-=V^+=0$
3. On a donc $V^-=0=\frac{\frac{V_e}{R_1}+\frac{V_s}{R_2}}{\frac{1}{R_1}+\frac{1}{R_2}}$ d'où $\frac{V_e}{R_1}+\frac{V_s}{R_2}=0$
$\frac{V_s}{R_2}=-\frac{V_e}{R_1}$ d'où $\frac{V_s}{V_e}=-\frac{R_2}{R_1}$
4. $\frac{V_s}{V_e}=-\frac{R_2}{R_1}$ $\implies \frac{V_s}{V_e}=-\frac{9K\Omega}{3K\Omega}=-3$
5. On a
- $V_{R_1}=R_1I=V_e-V^- \implies I=\frac{V_e-V^-}{R_1}$
- $V_{R_2}=-R_2I=V_s-V^-\implies I=\frac{-(V_s-V^-)}{R_2}$
D'où $\frac{V_e-V^-}{R_1}=\frac{-(V_s-V^-)}{R_2}$ et $V^+=V^-=0$ donc $\frac{V_e}{R_1}=\frac{-V_s}{R_2}$ et $\boxed{\frac{V_s}{V_e}=-\frac{R_2}{R_1}}$

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---
excalidraw-plugin: parsed
tags: [excalidraw]
---
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
# Excalidraw Data
## Text Elements
y ^RDbsTBLI
## Embedded Files
ea6ee8c28250e874006c0fe8f087216b9c8e5c82: $$V_B$$
688f9e6381aee37a8da56a0a1fe7db760c50936f: $$V_A$$
e6c4fac01398ed01f5a7e6df7a29a59d2e6a8172: $$V_C$$
3d1d4313d3e4c3a7184e274bf2574404a0bff62f: $$R_B$$
322c2c8404ee4a5fb6ff89fb95106a55d7f6dbb3: $$R_A$$
d3ac740bc90fdaf7af978372c437a22a5183f82f: $$R_C$$
%%
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```
%%