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university/S1/ExPhyI/.ipynb_checkpoints/ha3-checkpoint.ipynb
2025-04-16 10:50:38 +02:00

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"cells": [
{
"cell_type": "markdown",
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"source": [
"# Hausaufgabe Blatt 3\n",
"## Gleichförmig beschleunigte, geradlinige Bewegung - Revisited\n",
"\n",
"In dieser Aufgabe werden wir die Bahnkurve eines gleichförmig beschleunigten Objektes in einer Dimension berechnen und dieses mal auch visualisieren. Die Position $x$ zum Zeitpunkt $t$ ist, wie auf dem Blatt 2, gegeben durch folgende Gleichung:\n",
"\\begin{equation*}\n",
"x\\!\\left( t \\right) = x_0 + v_0 t + \\frac{1}{2} a t^2 \n",
"\\end{equation*}\n",
"wobei $x_0$ und $v_0$ die Anfangsposition und -geschwindigkeit sind und $a$ die konstante Beschleunigung, die auf das Objekt wirkt. \n",
"\n",
"## 1. Numpy Arrays: Linspace\n",
"Anstelle, dass wir die Einträge in numpy arrays \"per Hand\" definieren, können wir eine nützliche Funktion verwenden. \n",
"\n",
"**a)** \n",
"Machen Sie sich mit der nachstehenden Zelle vertraut. Verstehen Sie die Syntax?"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-01T10:22:27.227336Z",
"start_time": "2019-11-01T10:22:27.100666Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[0. 0.25 0.5 0.75 1. ]\n"
]
}
],
"source": [
"import numpy as np # Laden der Numpy Bibliothek \n",
"\n",
"x = np.linspace(0, 1, 5) # Definieren von x\n",
"\n",
"print(x) # Ausgabe x"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**b)** Erstellen sie ein numpy array für die Zeit `t` indem sie `np.linspace()` korrekt verwenden. Dabei soll gelten $t_0 = 0$ und $t_N = 5$ mit der Anzahl der Einträge $N = 50$."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**c)** Benutzen Sie die in ha2 Aufgabe 2 definierte Funktion `printBahnkurve()` um sich nun die Bahnkurve für das gerade erstellte array `t` ausgeben zu lassen. Verwenden Sie die Werte $x_0=3$ und $v_0=10$ wie auf Blatt 2."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Return\n",
"\n",
"Bisher hat unsere definierte Funktion lediglich einen `print()` Befehl ausgeführt. Wir wollen nun, dass unsere Funktion einen Wert zurück gibt. Dadurch kann der Wert in einer Variablen gespeichert und somit weiterverarbeitet werden. Dazu verwenden wir das `return` Statement. \n",
"\n",
"**d)** Betrachten Sie die folgenden zwei Funktionen. Beschreiben Sie kurz (1-2 Sätze), was hier geschieht. "
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-01T10:22:27.233313Z",
"start_time": "2019-11-01T10:22:27.230416Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2 4\n"
]
}
],
"source": [
"def identity(x): # definiere Funktion\n",
" return x # definiere Ausgabe\n",
"\n",
"def square(x):# definiere Funktion\n",
" return x**2 # definiere Ausgabe\n",
"\n",
"id2 = identity(2) # definiere id2 über Zugriff auf identity\n",
"square2 = square(2)# definiere id2 über Zugriff auf square\n",
"\n",
"print(id2, square2) # Ausgabe der Werte"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**e)** Schreiben Sie eine neue Funktion, indem Sie den `print()` Befehl in der Funktion `printBahnkurve()` durch das `return` Statement ersetzen. Wählen Sie einen geeigneten Namen für die neue Funktion. "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Visualisierung\n",
"Da Sie nun dazu in der Lage sind, viele Datenpunkte zu erzeugen, wollen wir als nächsten Schritt die berechnete Bahnkurve in einem plot mithilfe von `matplotlib.pyplot` visualisieren. `Matplotlib` ist eine beliebte und sehr vielseitige plot Bibliothek, die es uns ermöglicht Daten zu visualisieren. Wer einen Eindruck davon gewinnen möchte, was alles mit `matplotlib` möglich ist, kann ja mal [hier](https://matplotlib.org/3.1.1/gallery/index.html) vorbeischauen!\n",
"\n",
"Wir haben folgendes Grundgerüst vorbereitet, in dem die Funktion $f(x) = x^2$ beispielhaft geplottet wird."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-01T10:22:42.277126Z",
"start_time": "2019-11-01T10:22:42.160402Z"
}
},
"outputs": [
{
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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt # lade matplotlib als Bibliothek\n",
"import numpy as np\n",
"x = np.linspace(-2, 2, 170) # definiere x\n",
"xQuadrat = x**2 # berechen x^2\n",
"\n",
"# ### Anfang Grundgerüst ( mit # kann man Kommentare schreiben )\n",
"\n",
"fig, ax = plt.subplots()\n",
"\n",
"ax.set_title(\"Parabel\") # Titel\n",
"ax.set_xlabel(\"X-Werte\") # x-Achsenbeschriftrung\n",
"ax.set_ylabel(\"y-Werte\") # y-Achsenbeschriftung\n",
"\n",
"ax.plot(x, xQuadrat) # x-Wert hier: x, y Wert hier: xQuadrat\n",
"\n",
"plt.show()\n",
"\n",
"# ### Ende Grundgerüst"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**a)** Machen Sie sich mit dem Grundgerüst vertraut, indem Sie \n",
" - `x` mit Werten Ihrer Wahl erweitern\n",
" - einen geeigneten Titel\n",
" - geeignete x- und y- Achsenbeschriftung wählen.\n",
" \n",
"Möchte man mehrere Kurven in einem Diagramm darstellen, so muss `ax.plot()` lediglich erneut aufgerufen werden. \n",
"Dabei ist es nützlich diese Kurven in einer Legende zu unterscheiden:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-01T10:22:27.961375Z",
"start_time": "2019-11-01T10:22:27.514251Z"
}
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots()\n",
"\n",
"ax.set_title(\"Mehrfachplot\") # Titel\n",
"ax.set_xlabel(\"X\") #x-Achsenbeschriftung\n",
"ax.set_ylabel(\"Y\") # y-Achsenbeschriftung\n",
"\n",
"ax.plot(x, xQuadrat, label=\"$x^2$\") # label: Eintrag Legende, versteht auch LaTex!\n",
"ax.plot(x, x**4, label=\"$x^4$\") # label\n",
"\n",
"ax.legend() # Zeige Legende\n",
"plt.show() "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**b)** Kopieren Sie das Grundgerüst und ersetzen sie die x-Werte durch das oben definierte array `t` und die y-Werte durch die errechnete Bahnkurve. Wählen Sie auch hier einen geeigneten Titel und Achsenbeschriftungen."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-01T10:21:24.775267Z",
"start_time": "2019-11-01T10:21:24.689518Z"
}
},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**c)** Variieren Sie nun die Anfangsgeschwindigkeit. Erstellen Sie zwei Kurven mit verschiedenen Bedingungen (z.B. $v_0 = 10$ und $v_0=20$). Vergleichen Sie die Kurven miteinander, indem Sie diese in einem Diagramm darstellen. Benutzen Sie angemessene Beschriftungen!"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"ExecuteTime": {
"end_time": "2019-11-01T10:21:24.776711Z",
"start_time": "2019-11-01T10:21:24.023Z"
}
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.11.9"
},
"latex_envs": {
"LaTeX_envs_menu_present": true,
"autoclose": true,
"autocomplete": true,
"bibliofile": "biblio.bib",
"cite_by": "apalike",
"current_citInitial": 1,
"eqLabelWithNumbers": true,
"eqNumInitial": 1,
"hotkeys": {
"equation": "Ctrl-E",
"itemize": "Ctrl-I"
},
"labels_anchors": false,
"latex_user_defs": false,
"report_style_numbering": false,
"user_envs_cfg": false
}
},
"nbformat": 4,
"nbformat_minor": 4
}