generated from Nabla/LU_template
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12
.gitignore
vendored
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12
.gitignore
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protokoll.aux
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protokoll.pdf
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protokoll.bbl
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protokoll.run.xml
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protokoll.synctex.gz
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protokoll.blg
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protokoll-blx.bib
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protokoll.log
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.DS_Store
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protokoll.fls
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protokoll.fdb_latexmk
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res/graphs/__pycache__
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protokoll.bib
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protokoll.bib
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62
protokoll.tex
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protokoll.tex
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% !TeX spellcheck = en_US
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\documentclass[11pt]{article}
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\usepackage[
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backend=bibtex,
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style=numeric,
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sorting=ynt
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]{biblatex}
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\addbibresource{protokoll.bib}
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\usepackage{lipsum,caption,graphicx,subcaption}
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\usepackage{multicol}
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\usepackage{listings}
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\usepackage{amsmath}
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\usepackage[noabbrev, nameinlink]{cleveref}
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\usepackage{array,tabularx,calc}
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\usepackage{enumitem}
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\usepackage{amsfonts}
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\usepackage{pdfpages}
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\usepackage{fancyhdr}
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\usepackage[ngerman]{babel}
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\graphicspath{ {res/} }
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\usepackage[absolute,overlay]{textpos}
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\newlength{\conditionwd}
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\newenvironment{conditions}[1][where:\\]
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{%
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#1\tabularx{\textwidth-\widthof{#1}}[t]{
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>{$}l<{$} @{${}...{}$} X@{}
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}%
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}
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{\endtabularx\\[\belowdisplayskip]}
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\input{titlepage.tex}
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\begin{document}
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\deckblatt{Titel}{Koch, Markus}{7}{Rosa Posch}{Sally Marcher}{12403619}{12412869}{Datum}{Kennzahl}
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\section{Aufgabenstellung}
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\section{Voraussetzungen und Grundlagen}
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\section{Beschreibung der Versuchsanordnung}
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\section{Geräteliste}
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\section{Versuchsdurchführung und Messergebnisse}
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\section{Auswertung}
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\section{Diskussion}
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\section{Zusammenfassung}
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\section{Literatur}
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\printbibliography
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\end{document}
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BIN
res/deckblatt.pdf
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BIN
res/deckblatt.pdf
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53
res/graphs/example.py
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res/graphs/example.py
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from saplotlib import match_t, eval_uncert, symbolize, plot_dataset
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import numpy as np
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from sympy import sqrt, pi
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from sympy import *
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import matplotlib.pyplot as plt
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from scipy.optimize import curve_fit
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# => Value Prep:
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# Time for 10 Periods, [s]
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m_t = [13.49, 13.42, 13.51, 13.42, 13.45]
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t = np.mean(m_t) / 10 # convert to period time
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dt = (np.std(m_t, ddof=1)*match_t(m_t, 1) + 0.01) / 10
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# (Type A uncert + type B uncert)
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# Len of the pendulum
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d = (560 - 9.5)*1e-3
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dd = (2 + 0.5)*1e-3
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# Ablese- + Eichuncert.
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# Defining function
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def g(d, t):
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return d / (t/(2*np.pi))**2
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# Define params
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args = {"d":(d, dd), "t":(t, dt)}
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# Result
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print(eval_uncert(g, args))
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# Plotting Example:
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d = np.array([56, 50, 45, 40, 35, 30, 25, 20, 15, 10])*1e-2
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t = np.array([13.49, 13.33, 12.68, 11.91, 11.31, 10.32, 9.23, 8.36, 7.16, 5.73])/10
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def calc_dt(t):
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# Fixed from prev. example
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global dt
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return dt
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def calc_dd(d):
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# Ablese- + Eichuncert.
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return (2 + 0.5)*1e-3
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def T(l, g):
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return 2*pi*sqrt(l/g)
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plot_dataset(d,t,calc_dd(t),calc_dt(d),T,"Rohdaten")
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plt.title("Periodendauer eines Pendels")
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plt.ylabel("Periodendauer $T$ [s]")
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plt.xlabel("Länge $l$ [m]")
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plt.legend()
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plt.show()
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87
res/graphs/saplotlib.py
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res/graphs/saplotlib.py
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import numpy as np
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from scipy.optimize import curve_fit
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import matplotlib.pyplot as plt
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from sympy import *
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plt.rcParams['text.usetex'] = True
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# student_t_dict, values from [1]
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# keys are N-samples and entrys are for [sigma, 2*sigma, 3*sigma] => [68.3%, 95.5%, 99.7%]
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student_t_dict = {
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2:[1.84, 13.97, 235.8],
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3:[1.32, 4.53, 19.21],
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4:[1.20, 3.31, 9.22],
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5:[1.15, 2.87, 6.62],
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6:[1.11, 2.65, 5.51],
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8:[1.08, 2.43, 4.53],
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10:[1.06, 2.32, 4.09],
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20:[1.03, 2.14, 3.45],
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30:[1.02, 2.09, 3.28],
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50:[1.01, 2.05, 3.16],
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100:[1.00, 2.03, 3.08],
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200:[1.00, 2.01, 3.04]
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}
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def match_t(arr, sigma_mult):
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t = sigma_mult
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for i in range(0, len(student_t_dict)-1):
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if (list(student_t_dict.keys())[i] <= len(arr) < list(student_t_dict.keys())[i+1]):
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t = student_t_dict[list(student_t_dict.keys())[i]][sigma_mult-1]
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print(f"Matched Student t multiplier: {t}! Using {sigma_mult} Sigma width!")
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return t
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def symbolize(func):
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"""
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Arguments:
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func - function to symbolize
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Returns:
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sympy symbolized function
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"""
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return func(*[Symbol(label) for label in func.__code__.co_varnames])
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def conv_to_f_args(args):
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f_args = {}
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for key in args.keys():
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f_args[key] = args[key][0]
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return f_args
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def calc_uncert(symf, args, typ):
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if not (typ in ("A", "B")):
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raise ValueError('typ can only be "A" or "B"')
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symbols = symf.free_symbols
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f_args = conv_to_f_args(args)
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parts = {}
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sum = 0
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for s in symbols:
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part = abs(diff(symf, s).evalf(subs=f_args)) * args[str(s)][1]
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parts[str(s)] = part
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if(typ == "B"):
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sum += part
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else:
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sum += part**2
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return sum if(typ == "B") else sqrt(sum), parts
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def eval_uncert(f, args, typ="B"):
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symf = symbolize(f)
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uncert, _ = calc_uncert(symf, args, typ)
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f_args = conv_to_f_args(args)
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result = symf.evalf(subs=f_args)
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return result, uncert
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def plot_dataset(x, y, xerr, yerr, func, label, n=100, log=0):
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symfunc = symbolize(func)
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plt.errorbar(x, y, yerr=yerr, xerr=xerr, marker="o", ls="", capsize=5, label=label)
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if log:
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fitx = np.logspace(min(x), max(x), n)
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else:
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fitx = np.linspace(min(x), max(x), n)
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symbols = func.__code__.co_varnames
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npfunc = lambdify(symbols, symfunc, "numpy")
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popt, pcov = curve_fit(npfunc, x, y)
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plt.plot(fitx, npfunc(fitx, *popt), label="Fit: $"+latex(symfunc)+"$")
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print(f"Optimized {symbols[1:]} with values {popt}")
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"""
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Sources:
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[1] Skriptum zu "Einfuehrung in die physikalischen Messmethoden", Institut fuer Experimentalphysik, Graz, Maerz 2025
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"""
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titlepage.tex
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titlepage.tex
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\pagestyle{fancy}
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\newcommand{\deckblatt}[9]{
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\lhead{Gruppe #3, #4 \& #5}
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\rhead{#8}
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% Übungstitel
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\begin{textblock*}{12.4cm}[0,1](5.7cm,16.3cm)
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\centering
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\LARGE
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#1
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\end{textblock*}
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% Betreuer
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\begin{textblock*}{12.4cm}[0,1](5.7cm,17.35cm)
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\centering
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\LARGE
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#2
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\end{textblock*}
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% Gruppennummer
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\begin{textblock*}{2.3cm}[0,1](7.35cm,19.75cm)
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\centering
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\Huge
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#3
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\end{textblock*}
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% Name 1
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\begin{textblock*}{4.6cm}[0,1](5.3cm,22.2cm)
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\centering
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\Large
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#4
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\end{textblock*}
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% Name 2
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\begin{textblock*}{4.6cm}[0,1](12.25cm,22.2cm)
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\centering
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\Large
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#5
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\end{textblock*}
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% Kennzahl
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\begin{textblock*}{7.7cm}[0,1](3.2cm,23.8cm)
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\centering
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\Large
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#9
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\end{textblock*}
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% MtrNr 1
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\begin{textblock*}{3cm}[0,1](12.5cm,23.8cm)
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\centering
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\Large
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#6
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\end{textblock*}
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% MtrNr 2
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\begin{textblock*}{3.9cm}[0,1](15cm,23.8cm)
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\centering
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\Large
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#7
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\end{textblock*}
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% Datum
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\begin{textblock*}{7.7cm}[0,1](3.2cm,25.4cm)
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\centering
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\Large
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#8
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\end{textblock*}
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% Jahr
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\begin{textblock*}{3.35cm}[0,1](10.5cm,25.4cm)
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\centering
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\Large
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2025
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\end{textblock*}
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\includepdf{res/deckblatt.pdf}
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}
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