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diff --git a/fiz/vaje/10/dokument.lyx b/fiz/vaje/10/dokument.lyx new file mode 100644 index 0000000..bf0df5c --- /dev/null +++ b/fiz/vaje/10/dokument.lyx @@ -0,0 +1,1251 @@ +#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 +Vsiljeno nihanje in resonanca +\end_layout + +\begin_layout Author + +\noun on +Anton Luka Šijanec +\end_layout + +\begin_layout Date +29. + marec 2023 +\end_layout + +\begin_layout Abstract +Grafi in rezultati desete in zadnje vaje pri predmetu +\noun on +F41 +\noun default + na Gimnaziji Bežigrad v 4. + letniku. +\end_layout + +\begin_layout Section* +Podatki in grafi +\end_layout + +\begin_layout Standard +Teoretični model +\begin_inset Formula $s_{0}\left(\nu\right)$ +\end_inset + + harmoničnega nihala s tremi parametri je +\begin_inset Formula +\[ +s_{0}=\frac{A}{\sqrt{\left(B^{2}-\omega^{2}\right)^{2}+C^{2}\omega^{2}}}\text{{,}} +\] + +\end_inset + + +\end_layout + +\begin_layout Standard +kjer je +\begin_inset Formula $\omega=2\pi v$ +\end_inset + + oziroma, če jo izračunamo iz podatkov matematičnega nihala, +\begin_inset Formula $\omega=\sqrt{\frac{g}{l}}$ +\end_inset + +. +\end_layout + +\begin_layout Standard +\begin_inset Float table +placement H +wide false +sideways false +status open + +\begin_layout Plain Layout + +\lang english +\begin_inset Tabular +<lyxtabular version="3" rows="17" columns="4"> +<features tabularvalignment="middle"> +<column alignment="left" valignment="top" width="0pt"> +<column alignment="left" valignment="top" width="0pt"> +<column alignment="left" valignment="top" width="0pt"> +<column alignment="left" valignment="top" width="0pt"> +<row> +<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +\begin_inset Formula $l\left[\si{\meter}\right]$ +\end_inset + + +\end_layout + +\end_inset +</cell> +<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $x_{0}\left[\si{\meter}\right]$ +\end_inset + + +\end_layout + 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Text + +\begin_layout Plain Layout + +\lang english +4,952272 +\end_layout + +\end_inset +</cell> +<cell alignment="left" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +0,788179 +\end_layout + +\end_inset +</cell> +</row> +<row> +<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +0,5 +\end_layout + +\end_inset +</cell> +<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +0,009038 +\end_layout + +\end_inset +</cell> +<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +4,429447 +\end_layout + +\end_inset +</cell> +<cell alignment="left" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +0,704968 +\end_layout + +\end_inset +</cell> +</row> +<row> +<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +0,45 +\end_layout + +\end_inset +</cell> +<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +0,009038 +\end_layout + +\end_inset +</cell> +<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +4,669047 +\end_layout + +\end_inset +</cell> +<cell alignment="left" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +0,743102 +\end_layout + +\end_inset +</cell> +</row> +<row> +<cell 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+\begin_inset Text + +\begin_layout Plain Layout + +\lang english +1,039419 +\end_layout + +\end_inset +</cell> +</row> +<row> +<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +0,22 +\end_layout + +\end_inset +</cell> +<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +0,054231 +\end_layout + +\end_inset +</cell> +<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +6,677642 +\end_layout + +\end_inset +</cell> +<cell alignment="left" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +1,06278 +\end_layout + +\end_inset +</cell> +</row> +<row> +<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +0,21 +\end_layout + +\end_inset +</cell> +<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +0,056038 +\end_layout + +\end_inset +</cell> +<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +6,834785 +\end_layout + +\end_inset +</cell> +<cell alignment="left" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +1,08779 +\end_layout + +\end_inset +</cell> +</row> +<row> +<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +0,2 +\end_layout + +\end_inset +</cell> +<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +0,047 +\end_layout + +\end_inset +</cell> +<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +7,003571 +\end_layout + +\end_inset +</cell> +<cell alignment="left" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +1,114653 +\end_layout + +\end_inset +</cell> +</row> +<row> +<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +0,19 +\end_layout + +\end_inset +</cell> +<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +0,043385 +\end_layout + +\end_inset +</cell> +<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +7,185512 +\end_layout + +\end_inset +</cell> +<cell alignment="left" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +1,14361 +\end_layout + +\end_inset +</cell> +</row> +<row> +<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +0,18 +\end_layout + +\end_inset +</cell> +<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +0,043385 +\end_layout + +\end_inset +</cell> +<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +7,382412 +\end_layout + +\end_inset +</cell> +<cell alignment="left" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +1,174947 +\end_layout + +\end_inset +</cell> +</row> +<row> +<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +0,17 +\end_layout + +\end_inset +</cell> +<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +0,036154 +\end_layout + +\end_inset +</cell> +<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +7,596439 +\end_layout + +\end_inset +</cell> +<cell alignment="left" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +1,209011 +\end_layout + +\end_inset +</cell> +</row> +<row> +<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +0,16 +\end_layout + +\end_inset +</cell> +<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +0,032538 +\end_layout + +\end_inset +</cell> +<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +7,83023 +\end_layout + +\end_inset +</cell> +<cell alignment="left" valignment="top" topline="true" leftline="true" rightline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +1,24622 +\end_layout + +\end_inset +</cell> +</row> +<row> +<cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +0,15 +\end_layout + +\end_inset +</cell> +<cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +0,036154 +\end_layout + +\end_inset +</cell> +<cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +8,087027 +\end_layout + +\end_inset +</cell> +<cell alignment="left" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none"> +\begin_inset Text + +\begin_layout Plain Layout + +\lang english +1,28709 +\end_layout + +\end_inset +</cell> +</row> +</lyxtabular> + +\end_inset + + +\end_layout + +\begin_layout Plain Layout +\align center +\begin_inset Caption Standard + +\begin_layout Plain Layout +Izmerjeni in izračunani podatki. + Podatek o amplitudi je natančen na milimeter. +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Note Note +status open + +\begin_layout Plain Layout +\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=$s_0$, domain=0:12, ytick pos=left, samples=2 +56, xlabel=$ +\backslash +omega$, xtick pos=bottom, xmin=0, xmax=12, ymin=0, ymax=.06, +\end_layout + +\begin_layout Plain Layout + +%grid=both +\end_layout + +\begin_layout Plain Layout + +, major grid style={dashed,blue}] +\end_layout + +\begin_layout Plain Layout + + +\backslash +addplot[only marks] table [x=omega, y=x, col sep=comma] {podatki.csv}; +\end_layout + +\begin_layout Plain Layout + + +\backslash +addlegendentry{meritve} +\end_layout + +\begin_layout Plain Layout + + +\backslash +addplot[blue] (x, {0.47583543/sqrt(-6.87050654^2-x^2)^2+1.2365817^2*x^2}); +\end_layout + +\begin_layout Plain Layout + + +\backslash +addlegendentry{$A=0.47583543$, $B=-6.87050654$, $C=1.2365817$} +\end_layout + +\begin_layout Plain Layout + +\end_layout + +\begin_layout Plain Layout + +% +\backslash +addplot[mark=square*, blue, only marks] table [x=u, y=i, col sep=comma] + {2.csv}; +\end_layout + +\begin_layout Plain Layout + +% +\backslash +addlegendentry{zaporedno} +\end_layout + +\begin_layout Plain Layout + +% +\backslash +addplot[blue] (x, {x*1.1889}); +\end_layout + +\begin_layout Plain Layout + +% +\backslash +addlegendentry{} +\end_layout + +\begin_layout Plain Layout + +% +\backslash +addplot[mark=diamond*, green, only marks] table [x=u, y=i, col sep=comma] + {3.csv}; +\end_layout + +\begin_layout Plain Layout + +% +\backslash +addlegendentry{vzporedno} +\end_layout + +\begin_layout Plain Layout + +% +\backslash +addplot[blue] (x, {x*5.38536}); +\end_layout + +\begin_layout Plain Layout + +% +\backslash +addlegendentry{} +\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, ylabel=$b^{-1}$, ytick pos=right, samples=256, + xlabel=$a^{-1}$, xtick pos=top, %grid=both +\end_layout + +\begin_layout Plain Layout + +%, xlabel near ticks, ylabel near ticks, major grid style={dashed,red}, +\end_layout + +\begin_layout Plain Layout + +%legend style={at={(0.975,0.325)}, anchor=south east}, domain=4:7, xmin=4, + xmax=6.6, ymin=13, ymax=15.6 +\end_layout + +\begin_layout Plain Layout + +%] +\end_layout + +\begin_layout Plain Layout + +% +\backslash +addplot[mark=triangle*, red, only marks] table [x=1/a, y=1/b, col sep=comma] + {podatki.csv}; +\end_layout + +\begin_layout Plain Layout + +% +\backslash +addlegendentry{meritve} +\end_layout + +\begin_layout Plain Layout + +% +\backslash +addplot[red] (x, {1/0.0511438-x}); +\end_layout + +\begin_layout Plain Layout + +% +\backslash +addlegendentry{$b^{-1}=f^{-1}-a^{-1}$} +\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 + + +\begin_inset Formula $s_{0}\left(\omega\right)$ +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\end_inset + + +\end_layout + +\begin_layout Standard +\begin_inset CommandInset include +LatexCommand input +filename "graf.tex" + +\end_inset + + +\end_layout + +\begin_layout Standard +Iz grafa za harmonično nihanje razberemo 6,819 kot +\begin_inset Formula $\omega_{0}$ +\end_inset + +, kar pomeni, da je resonančna frekvenca matematičnega nihala +\begin_inset Formula $\SI{1,085}{\per\second}$ +\end_inset + +. +\end_layout + +\end_body +\end_document |