path: root/fiz/vaje/10/dokument.lyx

#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

\end_inset
</cell>
<cell alignment="left" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\lang english
\begin_inset Formula $\omega$
\end_inset


\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
\begin_inset Formula $\nu$
\end_inset


\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
0,4
\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
0,012654
\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
4,952272
\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 alignment="left" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout

\lang english
0,3
\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
0,025308
\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
5,718391
\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
0,91011
\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
0,35
\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
0,019885
\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
5,294202
\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
0,842598
\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
0,25
\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
6,264184
\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
0,996976
\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
0,24
\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
6,393356
\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
1,017534
\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
0,23
\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
6,530863
\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
1,039419
\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