forked from Sasserisop/MATH201
prepared to add support for displaying exalidraw drawings
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@ -37,12 +37,14 @@ $w(t)=\frac{1}{4}\mathcal{L}^{-1}\left\{ \frac{1}{s+1} - \frac{1}{s+5} \right\}+
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$=\underbrace{ \frac{1}{4}(e^{-t}-e^{ -5t }) }_{ \text{this came from initial conditions} }+\dots$
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$\mathcal{L}^{-1}\{e^{as}F(s)\}=f(t-a)u(t-a)$
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$$y(t)= \frac{1}{4}(e^{-t}-e^{ -5t }) +\frac{e}{4}u(t-1)(e^{ -(t-1) }-e^{ -5(t-1) })$$
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notice that this RHS came from the impulse delta and the effect it has on the system.
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notice that the right most term came from the impulse and the effect it had on the system.
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side note: delta functions are useful for quantum physics.
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Lets start modelling some electric circuits again:
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![[Drawing 2023-10-25 13.43.26.excalidraw]]
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$0.2I_{1}+0.1I_{3}'+2I_{1}=g(t)$
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the circuit is starts switched on and is then switched off at $t=1$
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Applying KVL:
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$0.2I_{1}+0.1I_{3}'+2I_{1}=g(t) \qquad \text{where } g(t)=\begin{cases}6, & 0\leq t\leq 1 \\0, & 1<t\end{cases}$
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$-I_{2}+0.1I_{3}'=0$
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$I_{1}=I_{2}+I_{3}$
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voila, a system of three equations.
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@ -0,0 +1,868 @@
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---
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excalidraw-plugin: parsed
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tags: [excalidraw]
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---
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==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠==
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# Text Elements
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%%
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# Drawing
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```compressed-json
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gAA=
|
||||
```
|
||||
%%
|
||||
Binary file not shown.
|
After Width: | Height: | Size: 40 KiB |
|
|
@ -0,0 +1,664 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠==
|
||||
|
||||
|
||||
# Text Elements
|
||||
%%
|
||||
# Drawing
|
||||
```compressed-json
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|
||||
```
|
||||
%%
|
||||
Binary file not shown.
|
After Width: | Height: | Size: 19 KiB |
|
|
@ -0,0 +1,558 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠==
|
||||
|
||||
|
||||
# Text Elements
|
||||
%%
|
||||
# Drawing
|
||||
```compressed-json
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```
|
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%%
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Binary file not shown.
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@ -0,0 +1,554 @@
|
|||
---
|
||||
|
||||
excalidraw-plugin: parsed
|
||||
tags: [excalidraw]
|
||||
|
||||
---
|
||||
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠==
|
||||
|
||||
|
||||
# Text Elements
|
||||
%%
|
||||
# Drawing
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```compressed-json
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||||
TCohSOMAfQOcE0AXOjhufa51ruOs93FtfdiTXkcN1rbh73GIiBhEbWKgpQU9r54d
|
||||
|
||||
tUzHb/T/wwM0C+XtfXbB/1/7mvajPBYiYjxQmHC8PsIuUzp92zeffs0Yu9+NlI/H
|
||||
|
||||
faOB4u0bT9jG+gayGrHiXfm16s+5LMjpyXyOyZJK5lUHNlVoUcRy3JZuMul8RBiA
|
||||
|
||||
kB67ZY1ebMqr4z9ciXgfk8FDmW7o+Vv6PS9OqmE5rcNf0yKhSTxp2eMjcbooYHjk
|
||||
|
||||
kua6pINXzbVmGZVlYju0lqP0dqZEJEDvomo7oTpkjR5JLizjeQYBO1yiKvtCM33q
|
||||
|
||||
3UQ4bZ3Py6tos4jaMLaILhRrJb5Z4cH0D4Auo2ALqB0AAwcBbgmgLqPoDeDMBlAD
|
||||
|
||||
wHUDBg+ztu0FtHLt0daIu9vd9/bqtYPeHfPOR7Jyt56xPKMuRp3D0n58xfnusWGj
|
||||
|
||||
S9poyvF+u3o/dkwQ2LGecNlAWxoMw9xJePdDHT3UBhGdfdTCQxRxD9Iube7iHo35
|
||||
|
||||
jRL2m0euA/zinqbPCW6q+Qas2h87BwQoA/SyBfBCoH6qA8ffWhW5zmO6E0Y+w/RX
|
||||
|
||||
cP885MCsXhZSwPPutBJ4yVI/Uwi0nRO1UuGnB63Wr55zG0J7sMieM7YnsysaMDXt
|
||||
|
||||
SMTMsK0Us53WMto+1pSQF1B1DMAdQtwYgA8HwBlxojUAfOGwD1DRVsLu14ie3cMG
|
||||
|
||||
d2Mjtz20zkbwWDvHTzpsJlMgwjun2DA36o76bnt/OHdz+5dwF5JWiSx+jZEnFmhd
|
||||
|
||||
f7vov/Ro90i7PtNNY9h9rMxe8VAJkcXgOmWY/b3U5eIdVLg/H2YLYWTyzNLo5l8e
|
||||
|
||||
q9HN6zjZl9S1p0iPIjjUKAGkI+SSpg7kYr7ZvWcubTMgTzyMFBc0Ic0jrjQYUlwZ
|
||||
|
||||
HlVfJaHMqu5LWdnM6vwrVMmdslqPGmOfC5h+9uasNriR6nuh2kyhtm9a89a5OvEx
|
||||
|
||||
b4Cda9PbYlNMLTC9sO/0SLaeKwVzN/0nt2+t1hhN9RME6lw5HoU/Xs/ON6GpT86Z
|
||||
|
||||
6/LW/cB0wJ0P3sDG2/B9GWycT4EYGTqfApg9AYgEIGIBiAc4pwTDgXC+xJGHvq3N
|
||||
|
||||
fR3cOvFre40Yvt2da+8XWnnzsl55pNKON1dtwP9fUxbB/Wh/nkPjJhxcrJBfPyW7
|
||||
|
||||
0YFC+av+8ov9K6HmAckviLMfGZlHlfaRlCRfobZAn2npmNqX73pPzS/sf8TLGq8X
|
||||
|
||||
yPRY+S2QU3yvnPCm/V6R1fJ9/cOo5Df/7OX/HwcSuW3nnp/BKxIQ7RZhcY3yrJwP
|
||||
|
||||
hEPKKBQqu/EII4z4xDjf58OpUDHji2zPnngzOMKDB4e4osFBCP+8UEchNe2rhjrj
|
||||
|
||||
ybXvq4RSnXoBqrmtaHlaTE9nG+aFSmtOtBzKBXLlo5W6tON6bKiGloYu+VJCAhMm
|
||||
|
||||
5vCM7pO1Vok5VGiJGzBpWV5rwE0BRJlwG6+HAQ66iBfrs46k6iJL454kCGmm5coN
|
||||
|
||||
qFybvmnquACkQTpnADYcUQBsDcA1sNAChgWQIcBEA3OI0AMAhAAgAUApwD37t8VQ
|
||||
|
||||
DYG2BCIBADYAIgC/C5gGwDwJPWc7g/oOBTgfgguBmQJYEQ+r0v54mBjgaQDOBrgd
|
||||
|
||||
mo4We1pc5eBoQT4GuB4IFtKb6ZQCEFhBmQAkHnC73kUAxBqQfoAAYp1naZZBKQXE
|
||||
|
||||
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|
||||
|
||||
FwWAFADWkRgTehHACAFUAu6FQb0FpBUQKQCDBoQWwAUAoYLgA+ChQU0FQALQV2CO
|
||||
|
||||
g1pPMGLBIQG5TPwKIHVx9w2ACiCggOcG7AwwvHDH74walJcrywJgcwAnB+oPgAis
|
||||
|
||||
8YCijJolorWjqc7sFkFGAbAAYA6BV6AQBp0/amUi6UkwesGuBeQXF6di9gfaAkA7
|
||||
|
||||
QZ0GGc7ZKQAkAmZHySnA+oG5TGgOoAkC4huIW8D2kewABgIAygKNBzuXYCsCUhlI
|
||||
|
||||
YSEQA9vMkFrB6QeiClBUAK0DIuaXGYDCAzAMFSohZ3h0GVAlNEfYkhjoEwBrgygI
|
||||
|
||||
CErg2QLgDLWrCMiBp0ewNgBEAcANwByhmbD6IGBaAKqEo4WztFiVAqoRbDgAPJM7
|
||||
|
||||
wgg5DKgDAA5sCADmwQAA
|
||||
```
|
||||
%%
|
||||
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Reference in New Issue