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author | Anton Luka Šijanec <anton@sijanec.eu> | 2022-11-17 00:21:55 +0100 |
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committer | Anton Luka Šijanec <anton@sijanec.eu> | 2022-11-17 00:21:55 +0100 |
commit | 0a39997c12f0d872413f6f08f16dfd65b191ccdd (patch) | |
tree | e69c170c49dbfdda50d13e21a2da5703cbd8c71a /fiz/vaje/4/dokument.lyx | |
parent | popravki fizikalne vaje (diff) | |
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Diffstat (limited to 'fiz/vaje/4/dokument.lyx')
-rw-r--r-- | fiz/vaje/4/dokument.lyx | 713 |
1 files changed, 713 insertions, 0 deletions
diff --git a/fiz/vaje/4/dokument.lyx b/fiz/vaje/4/dokument.lyx new file mode 100644 index 0000000..d2051d2 --- /dev/null +++ b/fiz/vaje/4/dokument.lyx @@ -0,0 +1,713 @@ +#LyX 2.3 created this file. For more info see http://www.lyx.org/ +\lyxformat 544 +\begin_document +\begin_header +\save_transient_properties true +\origin unavailable +\textclass article +\begin_preamble +\usepackage{siunitx} +\usepackage{pgfplots} +\usepackage{listings} +\usepackage{multicol} +\sisetup{output-decimal-marker = {,}, quotient-mode=fraction, output-exponent-marker=\ensuremath{\mathrm{3}}} +\end_preamble +\use_default_options true +\maintain_unincluded_children false +\language slovene +\language_package default +\inputencoding auto +\fontencoding global +\font_roman "default" "default" +\font_sans "default" "default" +\font_typewriter "default" "default" +\font_math "auto" "auto" +\font_default_family default +\use_non_tex_fonts false +\font_sc false +\font_osf false +\font_sf_scale 100 100 +\font_tt_scale 100 100 +\use_microtype false +\use_dash_ligatures true +\graphics default +\default_output_format default +\output_sync 0 +\bibtex_command default +\index_command default +\paperfontsize default +\spacing single +\use_hyperref false +\papersize default +\use_geometry true +\use_package amsmath 1 +\use_package amssymb 1 +\use_package cancel 1 +\use_package esint 1 +\use_package mathdots 1 +\use_package mathtools 1 +\use_package mhchem 1 +\use_package stackrel 1 +\use_package stmaryrd 1 +\use_package undertilde 1 +\cite_engine basic +\cite_engine_type default +\biblio_style plain +\use_bibtopic false +\use_indices false +\paperorientation portrait +\suppress_date false +\justification false +\use_refstyle 1 +\use_minted 0 +\index Index +\shortcut idx +\color #008000 +\end_index +\leftmargin 1cm +\topmargin 2cm +\rightmargin 1cm +\bottommargin 2cm +\headheight 1cm +\headsep 1cm +\footskip 1cm +\secnumdepth 3 +\tocdepth 3 +\paragraph_separation indent +\paragraph_indentation default +\is_math_indent 0 +\math_numbering_side default +\quotes_style german +\dynamic_quotes 0 +\papercolumns 1 +\papersides 1 +\paperpagestyle default +\tracking_changes false +\output_changes false +\html_math_output 0 +\html_css_as_file 0 +\html_be_strict false +\end_header + +\begin_body + +\begin_layout Title +Dušeno nihanje nitnega nihala +\end_layout + +\begin_layout Author + +\noun on +Anton Luka Šijanec +\end_layout + +\begin_layout Date +16. + november 2022 +\end_layout + +\begin_layout Abstract +Poročilo četrte vaje pri predmetu +\noun on +F41 +\noun default + na Gimnaziji Bežigrad v 4. + letniku. + Vaja je potekala 13. + oktobra 2022. +\end_layout + +\begin_layout Standard +\begin_inset CommandInset toc +LatexCommand tableofcontents + +\end_inset + + +\end_layout + +\begin_layout Section +Zveza med amplitudo hitrosti in amplitudo odmika +\end_layout + +\begin_layout Subsection +Naloga +\end_layout + +\begin_layout Standard +Razišči zvezo med amplitudo hitrosti in amplitudo odmika pri nihanju nitnega + nihala. +\end_layout + +\begin_layout Subsection +Potek dela +\end_layout + +\begin_layout Enumerate +Ko je nihalo v ravnovesni legi, nastavi ničlo slednika gibanja. +\end_layout + +\begin_layout Enumerate +S pomočjo slednika gibanja zajemi podatke za +\begin_inset Formula $\SI{60}{\second}$ +\end_inset + + dušenega nihanja nitnega nihala. +\end_layout + +\begin_layout Enumerate +Na vsake štiri nihaje odčitaj amplitudo odmika in amplitudo hitrosti in + podatke zapiši v tabelo. + Ker nihalo nima največje hitrosti, ko je odmik največji, odčitavaj največjo + hitrost vedno četrt nihaja prej kot največji odmik. +\end_layout + +\begin_layout Enumerate +Nariši graf amplitude hitrosti +\begin_inset Formula $v_{0}$ +\end_inset + + v odvisnosti od amplitude odmika +\begin_inset Formula $x_{0}$ +\end_inset + +! Določi naklon grafa in oceni nenatančnost te vrednosti. +\begin_inset Newline newline +\end_inset + + +\begin_inset ERT +status open + +\begin_layout Plain Layout + + +\backslash +begin{lstlisting} +\end_layout + +\begin_layout Plain Layout + +fit (x*p) "v_od_x.tsv" using 1:2 via p +\end_layout + +\begin_layout Plain Layout + + +\backslash +end{lstlisting} +\end_layout + +\end_inset + + +\begin_inset Formula +\[ +p=\SI{4,52127}{\per\second}\pm\SI{0,1111}{\per\second} +\] + +\end_inset + + +\end_layout + +\begin_layout Enumerate +Iz grafa +\begin_inset Formula $x(t)$ +\end_inset + + določi +\begin_inset Formula $t_{0}$ +\end_inset + + in določi nenatančnost te vrednosti. + Iz tako določenega +\begin_inset Formula $t_{0}$ +\end_inset + + in iz naklona grafa +\begin_inset Formula $v_{0}(x_{0})$ +\end_inset + + preveri zvezo +\begin_inset Formula $v_{0}=x_{0}2\pi/t_{0}$ +\end_inset + +. +\end_layout + +\begin_layout Standard +\begin_inset Formula +\[ +t_{0_{\text{{odčitan}}}}=\frac{{t}}{n}=\SI{1,2806}{\second} +\] + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Formula +\[ +t_{0_{\text{{izračunan}}}}=\frac{{2\pi}}{p}=\SI{1,38969}{\second} +\] + +\end_inset + + +\end_layout + +\begin_layout Standard +Red velikosti je enak, vendar se rešitvi razlikujeta. + Najverjetneje so bili med zaznavanjem prehodov čez nič za odčitanje +\begin_inset Formula $t_{0}$ +\end_inset + + iz grafa +\begin_inset Formula $x(t)$ +\end_inset + + lažni pozitivni odčitki. +\end_layout + +\begin_layout Standard +\begin_inset Float figure +placement H +wide false +sideways false +status open + +\begin_layout Plain Layout +\align center +\begin_inset ERT +status open + +\begin_layout Plain Layout + + +\backslash +begin{tikzpicture} +\end_layout + +\begin_layout Plain Layout + + +\backslash +begin{axis}[width=0.75 +\backslash +textwidth, scale only axis, ylabel=$v$, domain=-0.1:0.1, ytick pos=left, samples=2 +56, xlabel=$x$, xtick pos=bottom] +\end_layout + +\begin_layout Plain Layout + + +\backslash +addplot[red, only marks] table [x=x, y=v] {v_od_x.tsv}; +\end_layout + +\begin_layout Plain Layout + + +\backslash +addplot[green] (x, {x*(4.52127+0.1111)}); +\end_layout + +\begin_layout Plain Layout + + +\backslash +addplot[green] (x, {x*(4.52127-0.1111)}); +\end_layout + +\begin_layout Plain Layout + + +\backslash +addplot[red] (x, {x*(4.52127)}); +\end_layout + +\begin_layout Plain Layout + + +\backslash +end{axis} +\end_layout + +\begin_layout Plain Layout + + +\backslash +end{tikzpicture} +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Plain Layout +\begin_inset Caption Standard + +\begin_layout Plain Layout +\begin_inset CommandInset label +LatexCommand label +name "fig:graf" + +\end_inset + +Graf amplitude hitrosti nihanja v odvisnosti od amplitude odmika nihala. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Section +Zmanjševanje amplitude pri dušenem nihanju +\end_layout + +\begin_layout Subsection +Naloga +\end_layout + +\begin_layout Standard +Potrdi, da se amplituda +\begin_inset Formula $x_{0}$ +\end_inset + + pri dušenem nihanju zmanjšuje eksponentno kot +\begin_inset Formula $x_{0}(t)=x_{00}e^{-\beta t}$ +\end_inset + +, kjer je +\begin_inset Formula $x_{00}$ +\end_inset + + amplituda nihala ob času +\series bold + +\begin_inset Formula $t=\SI{0}{\second}$ +\end_inset + + +\series default +, +\begin_inset Formula $\beta$ +\end_inset + + pa koeficient dušenja. +\end_layout + +\begin_layout Subsection +Potek dela +\end_layout + +\begin_layout Enumerate +Nariši graf amplitude hitrosti +\begin_inset Formula $x_{0}$ +\end_inset + + v odvisnosti od časa! Skozi točke na grafu +\series bold + +\begin_inset Formula $x_{0}(t)$ +\end_inset + + +\series default + nariši ustrezno eksponentno krivuljo! +\begin_inset Newline newline +\end_inset + + +\begin_inset ERT +status open + +\begin_layout Plain Layout + + +\backslash +begin{lstlisting} +\end_layout + +\begin_layout Plain Layout + +n=0.1 +\end_layout + +\begin_layout Plain Layout + +b=0.01 +\end_layout + +\begin_layout Plain Layout + +fit n*exp(-b*x) "v_od_x.tsv" using 3:4 via n, b +\end_layout + +\begin_layout Plain Layout + +fit (x*ln) "v_od_x.tsv" using 3:5 via ln +\end_layout + +\begin_layout Plain Layout + + +\backslash +end{lstlisting} +\end_layout + +\end_inset + + +\begin_inset Formula +\[ +n=x_{00}=\SI{0,0943867}{\meter}\pm\SI{0,001524}{\meter} +\] + +\end_inset + + +\begin_inset Formula +\[ +b=\SI{0,0441715}{\per\second}\pm\SI{0,001038}{\per\second}=\beta +\] + +\end_inset + + +\begin_inset Formula +\[ +ln=-\beta=\SI{-0,0467447}{\per\second}\pm\SI{0,001239}{\per\second} +\] + +\end_inset + + +\begin_inset Newline newline +\end_inset + + +\begin_inset Formula $b$ +\end_inset + + in +\begin_inset Formula $ln$ +\end_inset + +, torej +\begin_inset Formula $\beta$ +\end_inset + +, pridobljeni pred linearizacijo in po linearizaciji sta skoraj enaki. + Razlika med njima se pojavi samo zaradi namerne nenatančnosti računalnika. +\end_layout + +\begin_layout Enumerate +Nariši graf +\begin_inset Formula $\ln\left(\frac{x_{0}}{x_{00}}\right)$ +\end_inset + + v odvisnosti od časa in iz grafa določi koeficient dušenja +\begin_inset Formula $\beta$ +\end_inset + +. + Določitev napak v +\begin_inset Formula $\ref{enu:Nari=00003D000161i-graf-}.$ +\end_inset + + delu vaje ni potrebna. +\begin_inset CommandInset label +LatexCommand label +name "enu:Nariši-graf-" + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset Float figure +placement H +wide false +sideways false +status open + +\begin_layout Plain Layout +\align center +\begin_inset ERT +status open + +\begin_layout Plain Layout + + +\backslash +begin{tikzpicture} +\end_layout + +\begin_layout Plain Layout + + +\backslash +begin{axis}[width=0.75 +\backslash +textwidth, scale only axis, domain=0:60, ytick pos=left, samples=256, xlabel=$t$ +, xtick pos=bottom, ylabel=$ +\backslash +sqrt{x^2}$] +\end_layout + +\begin_layout Plain Layout + + +\backslash +addplot[only marks] table [x=t, y=absx] {v_od_x.tsv}; +\end_layout + +\begin_layout Plain Layout + + +\backslash +addplot[green] (x, {(0.0943867+0.001524)*exp((-0.0441715+ 0.001038)*x)}); +\end_layout + +\begin_layout Plain Layout + + +\backslash +addplot[green] (x, {(0.0943867-0.001524)*exp((-0.0441715- 0.001038)*x)}); +\end_layout + +\begin_layout Plain Layout + + +\backslash +addplot[black] (x, {0.0943867*exp(-0.0441715*x)}); +\end_layout + +\begin_layout Plain Layout + + +\backslash +end{axis} +\end_layout + +\begin_layout Plain Layout + + +\backslash +begin{axis}[width=0.75 +\backslash +textwidth, scale only axis, domain=0:60, xlabel near ticks, samples=16, + xlabel=$t$, ylabel near ticks, ytick pos=right, axis y line*=right, ylabel=$ +\backslash +ln +\backslash +frac{x_0}{x_{00}}$] +\end_layout + +\begin_layout Plain Layout + + +\backslash +addplot[red, only marks] table [x=t, y=ln] {v_od_x.tsv}; +\end_layout + +\begin_layout Plain Layout + + +\backslash +addplot[green] (x, {x*(-0.0467447+0.001239)}); +\end_layout + +\begin_layout Plain Layout + + +\backslash +addplot[green] (x, {x*(-0.0467447-0.001239)}); +\end_layout + +\begin_layout Plain Layout + + +\backslash +addplot[red] (x, {x*-0.0467447}); +\end_layout + +\begin_layout Plain Layout + + +\backslash +end{axis} +\end_layout + +\begin_layout Plain Layout + + +\backslash +end{tikzpicture} +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Plain Layout +\begin_inset Caption Standard + +\begin_layout Plain Layout +\begin_inset CommandInset label +LatexCommand label +name "fig:graf-1" + +\end_inset + +Graf amplitude nihanja (največjega odmika od osi) v odvisnosti od časa. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Section +Uporabljen program +\end_layout + +\begin_layout Standard +Za zaznavanje prehoda ničel in generiranje tabel sem spisal majhen program: +\end_layout + +\begin_layout Standard +\begin_inset ERT +status open + +\begin_layout Plain Layout + + +\backslash +lstinputlisting[language=Python]{preseki.py} +\end_layout + +\end_inset + + +\end_layout + +\end_body +\end_document |