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# ANGIELSKI |
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## Lekcja 1 - zadanie domowe | ||
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### zadanie 1 | ||
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1. premise | ||
2. fallacy | ||
3. claim | ||
4. rebut | ||
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### zadanie 2 | ||
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1. k | ||
2. | ||
3. l | ||
4. a | ||
5. b | ||
6. d | ||
7. c | ||
8. e | ||
9. i | ||
10. h | ||
11. f | ||
12. G |
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<!--This file is auto-generated by Makefile | ||
----DO NOT EDIT --> | ||
--- | ||
_Notatki z pliku `notes/eio/eio_0000.00.00.md`_ | ||
```{include} ../notes/eio/eio_0000.00.00.md | ||
``` | ||
--- | ||
_Notatki z pliku `notes/eio/eio_2024.02.27.md`_ | ||
```{include} ../notes/eio/eio_2024.02.27.md | ||
``` | ||
--- | ||
_Notatki z pliku `notes/eio/eio_2024.02.29.md`_ | ||
```{include} ../notes/eio/eio_2024.02.29.md | ||
``` |
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# Elektromagnetyzm i Optyka | ||
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### Fale Sprężyste | ||
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Rozpatrzmy mechanizm propagacji fali w pręcie (fala podłużna) (Eksperyment z wygiętym prętem w imadle). | ||
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Rozpatrzmy wycinek pręta ("Plasterek") przed dojściem impulsu falowego wycięty w odległości $A$ i $A'$, szerokości $dx$ wykonanego z materiału | ||
o gęstości $\rho$ | ||
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Po dojściu impulsu przekrój $A$ odchyli się o $\psi$. Ponieważ materiał jest sprężysty, przekrój $A'$ nie przesunie się o $\psi$ tylko o $d\psi$. | ||
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$$ | ||
m = \rho * s * dx \\ | ||
a = \frac{d^2 \psi}{dt^2} \\ | ||
dF = F - F' \\ | ||
dF = \rho * s * dx * \frac{d^2 \psi}{dt^2} \\ | ||
\bf{\frac{dF}{dx} = \rho * s * \frac{d^2 \psi}{dt^2}} \\ | ||
$$ | ||
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Teraz należy wykonać obliczenia zgodnie z prawem Hook'a | ||
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$$ | ||
P = E * \frac{d \psi}{dx} \\ | ||
F = E * s * \frac{d \psi}{dx} \\ | ||
\frac{F}{dx} = E * s * \frac{d^2 \psi}{dx^2} \\ | ||
\\ | ||
\frac{d^2 \psi}{dt^2} = \frac{E}{\rho} \frac{d^2 \psi}{dx^2} \\ | ||
v = \sqrt{\frac{E}{\rho}} | ||
$$ | ||
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### Ogólna Formuła na prędkość fali sprężystej | ||
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- rozchodzenie fali podłużnej w cieczy (lub gazie). | ||
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$$ | ||
v = \sqrt{\frac{K}{\rho}} | ||
$$ | ||
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- fala poprzeczna w pręcie (rozchodząca się na zasadzie mechanizmu ścinania). | ||
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$$ | ||
v = \sqrt{\frac{G}{\rho}} | ||
$$ | ||
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`G` to moduł sztywności. | ||
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```{admonition} Wzór Newtona | ||
Niech M oznacza odpowiedni moduł sprężystości, wtedy | ||
$$ | ||
v = \sqrt{\frac{M}{\rho}} | ||
$$ | ||
``` | ||
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- Fala poprzeczna na strunie | ||
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### Fale na powierzchni wody | ||
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$$ | ||
F = 2 \sigma l \\ | ||
$$ | ||
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Przybliżony wzór dla fal harmnoicznych | ||
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$$ | ||
v = \sqrt{\frac{g\lambda}{2\pi} +\frac{2\pi \sigma}{\rho \lambda}} | ||
$$ | ||
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Wzór jest adekwatny gdy głebokość zbiornika jest dużo większa od długości fali. | ||
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#### Ośrodek dyspersyjny | ||
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rozpatrzmy propagację fal bardzo długich. Można zauważyć, że w tym przypadku | ||
im większa długość fali $\lambda$ tym prędkość większa. | ||
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```{admonition} Ośrodek dyspersyjny | ||
Ośrodek dyspersyjny to taki, w którym prędkość rozchodzenia się fali | ||
zależy od długości fali | ||
``` | ||
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Pakiet falowy to połączenie fali harmonicznej (sinusoidalnej) z pojdeynczym impulsem falowym. | ||
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W środowisku dyspersyjnym pakiet falowy się rozpadnie (dystorsia). | ||
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$$ | ||
v = \lambda f = \frac{\omega}{k} | ||
$$ | ||
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Rozważamy pakiety falowe złożone z dwuch częstości. | ||
Dla pakietów o dowolnej liczbie składowych występuje prętkość grupowa $v_g = \frac{d \omega}{dk}$ | ||
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### Natężenie Fali | ||
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$I$ - powierzchniowa gęstość mocy $\left[\frac{W}{m^2}\right]$. |
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<!--This file is auto-generated by Makefile | ||
----DO NOT EDIT --> | ||
--- | ||
_Notatki z pliku `notes/eio_cw/eio_0000.00.00.md`_ | ||
```{include} ../notes/eio_cw/eio_0000.00.00.md | ||
``` | ||
--- | ||
_Notatki z pliku `notes/eio_cw/eio_2024.02.27.md`_ | ||
```{include} ../notes/eio_cw/eio_2024.02.27.md | ||
``` |
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# Elektromagnetyzm i Optyka - ĆWICZENIA | ||
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<!--This file is auto-generated by Makefile | ||
----DO NOT EDIT --> | ||
--- | ||
_Notatki z pliku `notes/ekonomia_menedzerska/ekonomia_menedzerska_2824.02.28.md`_ | ||
```{include} ../notes/ekonomia_menedzerska/ekonomia_menedzerska_2824.02.28.md | ||
``` |
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assets/notes/ekonomia_menedzerska/ekonomia_menedzerska_2824.02.28.md
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- wymyślamy inwestycje | ||
- założenia | ||
- analiza w układzie rocznym | ||
- źrudła inwestycji (kapitał włąsny/kredyt zaciągany w 2 transzach po roku) | ||
- |
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