prepared to add support for displaying exalidraw drawings

This commit is contained in:
Sasserisop 2023-10-27 09:50:38 -06:00
parent e4ce765132
commit 33c0ef8795
33 changed files with 19781 additions and 149717 deletions

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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\}+
$=\underbrace{ \frac{1}{4}(e^{-t}-e^{ -5t }) }_{ \text{this came from initial conditions} }+\dots$ $=\underbrace{ \frac{1}{4}(e^{-t}-e^{ -5t }) }_{ \text{this came from initial conditions} }+\dots$
$\mathcal{L}^{-1}\{e^{as}F(s)\}=f(t-a)u(t-a)$ $\mathcal{L}^{-1}\{e^{as}F(s)\}=f(t-a)u(t-a)$
$$y(t)= \frac{1}{4}(e^{-t}-e^{ -5t }) +\frac{e}{4}u(t-1)(e^{ -(t-1) }-e^{ -5(t-1) })$$ $$y(t)= \frac{1}{4}(e^{-t}-e^{ -5t }) +\frac{e}{4}u(t-1)(e^{ -(t-1) }-e^{ -5(t-1) })$$
notice that this RHS came from the impulse delta and the effect it has on the system. notice that the right most term came from the impulse and the effect it had on the system.
side note: delta functions are useful for quantum physics. side note: delta functions are useful for quantum physics.
Lets start modelling some electric circuits again: Lets start modelling some electric circuits again:
![[Drawing 2023-10-25 13.43.26.excalidraw]] ![[Drawing 2023-10-25 13.43.26.excalidraw]]
$0.2I_{1}+0.1I_{3}'+2I_{1}=g(t)$ the circuit is starts switched on and is then switched off at $t=1$
Applying KVL:
$0.2I_{1}+0.1I_{3}'+2I_{1}=g(t) \qquad \text{where } g(t)=\begin{cases}6, & 0\leq t\leq 1 \\0, & 1<t\end{cases}$
$-I_{2}+0.1I_{3}'=0$ $-I_{2}+0.1I_{3}'=0$
$I_{1}=I_{2}+I_{3}$ $I_{1}=I_{2}+I_{3}$
voila, a system of three equations. voila, a system of three equations.

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@ -0,0 +1,868 @@
---
excalidraw-plugin: parsed
tags: [excalidraw]
---
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠==
# Text Elements
%%
# Drawing
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---
excalidraw-plugin: parsed
tags: [excalidraw]
---
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠==
# Text Elements
%%
# Drawing
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---
excalidraw-plugin: parsed
tags: [excalidraw]
---
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠==
# Text Elements
%%
# Drawing
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---
excalidraw-plugin: parsed
tags: [excalidraw]
---
==⚠ Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠==
# Text Elements
%%
# Drawing
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