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diff --git a/.gitignore b/.gitignore
index 3dc5117..31500ee 100644
--- a/.gitignore
+++ b/.gitignore
@@ -4,3 +4,5 @@ fit.log
 core
 *.lyx~
 \#*.lyx#
+.RData
+.Rhistory
diff --git a/fiz/vaje/3/dokument.lyx b/fiz/vaje/3/dokument.lyx
new file mode 100644
index 0000000..194d065
--- /dev/null
+++ b/fiz/vaje/3/dokument.lyx
@@ -0,0 +1,1073 @@
+#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
+Energija prožne vzmeti
+\end_layout
+
+\begin_layout Author
+
+\noun on
+Anton Luka Šijanec
+\end_layout
+
+\begin_layout Date
+16.
+ november 2022
+\end_layout
+
+\begin_layout Abstract
+Poročilo tretje 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
+Naloga
+\end_layout
+
+\begin_layout Enumerate
+S pomočjo prožne vzmeti poženi leseno klado po vodoravni podlagi in opazuj,
+ na kakšni poti se ustavi.
+ Iz meritev določi koeficient vzmeti.
+\end_layout
+
+\begin_layout Enumerate
+Koeficient vzmeti določi tudi s pomočjo elektronske merilne tehtnice in
+ primerjaj obe vredosti.
+\end_layout
+
+\begin_layout Section
+Potrebščine
+\end_layout
+
+\begin_layout Itemize
+cev iz pleksi stekla z zatičem
+\end_layout
+
+\begin_layout Itemize
+vzmet
+\end_layout
+
+\begin_layout Itemize
+lesena klada
+\end_layout
+
+\begin_layout Itemize
+silomer
+\end_layout
+
+\begin_layout Itemize
+merilni trak
+\end_layout
+
+\begin_layout Itemize
+elektronska tehtnica
+\end_layout
+
+\begin_layout Section
+Potek dela
+\end_layout
+
+\begin_layout Subsection
+Izstreljevanje klade
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Izstreljevanje-klade"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Vzmet vstavi v cev iz pleksi stekla in zatič namesti v tako lego, da bo
+ iz cevi gledalo 
+\begin_inset Formula $\SI{3}{\centi\meter}$
+\end_inset
+
+ vzmeti.
+\end_layout
+
+\begin_layout Standard
+Pred vzmet postavi leseno klado in s klado stisni vzmet tako, da bo vsa
+ v cevi.
+\end_layout
+
+\begin_layout Standard
+Klado spusti in izmeri, kako daleč se premakne (
+\begin_inset Formula $s$
+\end_inset
+
+).
+ Meritev ponovi vsaj petkrat.
+\end_layout
+
+\begin_layout Standard
+Prestavi zatič za eno luknjo tako, da bo iz cevi gledal 
+\begin_inset Formula $\SI{1}{\centi\meter}$
+\end_inset
+
+ daljši kos vzmeti in ponovno izstreli klado.
+ Poskus ponavljaj na enak način z različnimi legami zatiča tako, da gleda
+ pri vsaki naslednji ponovitvi iz cevi 
+\begin_inset Formula $\SI{1}{\centi\meter}$
+\end_inset
+
+ daljši del vzmeti.
+ Vsako meritev petkrat ponovi.
+ Meritve zaključiš pri tisti dolžini vzmeti, ko klada doseže rob mize.
+\end_layout
+
+\begin_layout Standard
+Nariši graf premika klade po izstrelitvi (
+\begin_inset Formula $s$
+\end_inset
+
+) v odvisnosti od deformacije vzmeti pred izstrelitvijo (
+\begin_inset Formula $x$
+\end_inset
+
+) ter graf 
+\begin_inset Formula $s(x^{2})$
+\end_inset
+
+.
+ Iz naklona drugega grafa in izmerjene sile trenja izračunaj koeficient
+ uporabljene vzmeti.
+ Tako izračunani koeficient primerjaj z vrednostjo, ki si jo dobil pri meritvi
+ 
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "subsec:Določanje-koeficienta-s-tehtnico"
+plural "false"
+caps "false"
+noprefix "false"
+
+\end_inset
+
+.
+\begin_inset Formula 
+\[
+m_{\text{{klade}}}=\SI{193}{\gram}
+\]
+
+\end_inset
+
+
+\begin_inset Formula 
+\[
+m_{\text{{pleksi}}}=\SI{63,6}{\gram}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\[
+m_{\text{{vzmeti}}}=\SI{13,7}{\gram}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\[
+l_{\text{{vzmeti}}}=\SI{16,7}{\centi\meter}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\[
+l_{\text{{pleksi}}}=\SI{25}{\centi\meter}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\[
+l_{\text{{pleksi}}_{\text{{luknja0}}}}=\SI{8}{\centi\meter}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\[
+l_{\text{{pleksi}}_{\text{{\Delta med\ luknjami}}}}=\SI{1}{\centi\meter}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Vleka klade
+\end_layout
+
+\begin_layout Standard
+Z elastiko pripni na klado silomer in izmeri silo trenja pri premikanju
+ klade po mizi.
+ Oceni napako meritve.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\[
+F_{\text{{lepenja}}}=\SI{0,9}{\newton}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\[
+F_{\text{{trenja}}}=\SI{0,7}{\newton}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\[
+\overline{{F}}x=E=\frac{{1}}{2}kx^{2}=F_{\text{{trenja}}}s\rightarrow k=2\frac{{F_{\text{{trenja}}}s}}{x^{2}}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+begin{lstlisting}
+\end_layout
+
+\begin_layout Plain Layout
+
+fit (x*q)**2 "meritev.tsv" using 2:4 via q
+\end_layout
+
+\begin_layout Plain Layout
+
+fit (x*p) 
+\begin_inset Quotes gld
+\end_inset
+
+meritev.tsv
+\begin_inset Quotes grd
+\end_inset
+
+ using 3:4 via p
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+end{lstlisting}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Naklonski kot premice je 
+\begin_inset Formula $p=\SI{35,1}{\per\meter}\pm\SI{0,4462}{\per\meter}$
+\end_inset
+
+, koeficient vzmeti je torej po zgornji enačbi 
+\begin_inset Formula $k=2F_{\text{{trenja}}}p=\SI{51,2568}{\kilo\gram\per\second\squared}$
+\end_inset
+
+.
+ Za kvadratno krivuljo pa je 
+\begin_inset Formula $q=6,05079\pm0,03686$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Določanje koeficienta s tehtnico
+\begin_inset CommandInset label
+LatexCommand label
+name "subsec:Določanje-koeficienta-s-tehtnico"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Koeficient vzmeti določi še na drug način: vzmet vstavi v cev iz pleksija,
+ tako da je še nekaj gleda iz cevi in postavi vse skupaj navpično na elektronsko
+ tehtnico.
+ Preberi, kaj kaže tehtnica, ko vzmet v cevi samo stoji na tehtnici in koliko,
+ ko cev pritisneš navzdol, da se vzmet skrči.
+ Iz obeh odčitanih vrednosti in deformacije vzmeti izračunaj koeficient
+ vzmeti.
+ Meritev ponovi za vsaj štiri različne deformacije vzmeti.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\[
+k=\frac{F}{x}=\frac{{m_{\text{{kot\ jo\ kaže\ tehtnica}}}g}}{x}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula 
+\[
+\overline{{k}}=\SI{65,381}{\kilo\gram\per\second\squared}
+\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Čeprav je red velikosti na oba načina izmerjenega koeficienta vzmeti enak,
+ se pojavi razlika; predvidevam, da zato, ker se klada ustavi nekoliko prej,
+ kot bi se, če lepenja ne bi bilo.
+ Lepenje, izmerjeno 
+\begin_inset Formula $\SI{0,9}{\newton},$
+\end_inset
+
+ povzroči, da se telo ustavi prej, čeprav tega ne upoštevam pri računanju
+ energij, zato izgleda, kakor da je bilo vanjo vložene več energije.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float table
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Tabular
+<lyxtabular version="3" rows="8" columns="5">
+<features tabularvalignment="middle">
+<column alignment="center" valignment="top">
+<column alignment="center" valignment="top">
+<column alignment="center" valignment="top">
+<column alignment="center" valignment="top">
+<column alignment="center" valignment="top">
+<row>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $n_{\text{{luknje}}}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $x\text{\left[\si{\centi\meter}\right]}$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $s\left[\si{\meter}\right]$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $m_{\text{{kot\ jo\ kaže\ tehtnica}}}\left[\si{\gram}\right]$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+\begin_inset Formula $k_{\text{{iz\ naloge\ \ref{subsec:Dolo=00003D00003D00010Danje-koeficienta-s-tehtnico}}}}\left[\si{\kilo\gram\per\second\squared}\right]$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row>
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+\begin_layout Plain Layout
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+\end_inset
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+\begin_layout Plain Layout
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+\begin_layout Plain Layout
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+\begin_inset Text
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+\begin_layout Plain Layout
+620
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+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
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+\begin_layout Plain Layout
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+\end_layout
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+</row>
+</lyxtabular>
+
+\end_inset
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+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption Standard
+
+\begin_layout Plain Layout
+Meritve
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\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, ylabel=$s$, domain=0:0.1, ytick pos=left, samples=256
+, xlabel=$
+\backslash
+color{red}x
+\backslash
+color{black}$, xtick pos=bottom, ylabel=$s$]
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+addplot[red, only marks] table [x=x, y=s] {meritev.tsv};
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+addplot[green] (x, {((x*(6.05079+0.03686))^2});
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+addplot[green] (x, {((x*(6.05079-0.03686))^2});
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+addplot[red] (x, {((x*(6.05079))^2});
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+end{axis}
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+begin{axis}[width=0.75
+\backslash
+textwidth, scale only axis, xlabel near ticks, domain=0:0.01, samples=16,
+ xtick pos=bottom, xtick pos=top, axis x line*=top, xlabel=$x^2$]
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+addplot[only marks] table [x=x2, y=s] {meritev.tsv};
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+addplot[green] (x, {x*(36.612+0.4462)});
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+addplot[green] (x, {x*(36.612-0.4462)});
+\end_layout
+
+\begin_layout Plain Layout
+
+
+\backslash
+addplot[black] (x, {x*36.612});
+\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
+
+Grafa 
+\begin_inset Formula $s(x)$
+\end_inset
+
+ in 
+\begin_inset Formula $s(x^{2})$
+\end_inset
+
+.
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_body
+\end_document
diff --git a/fiz/vaje/3/meritev.tsv b/fiz/vaje/3/meritev.tsv
new file mode 100644
index 0000000..0165866
--- /dev/null
+++ b/fiz/vaje/3/meritev.tsv
@@ -0,0 +1,8 @@
+n	x	x2	s	m
+0	0.03	0.0009	0.028	190
+1	0.04	0.0016	0.05	260
+2	0.05	0.0025	0.096	340
+3	0.06	0.0036	0.13	400
+4	0.07	0.0049	0.174	470
+5	0.08	0.0064	0.24	540
+6	0.09	0.0081	0.297	620
diff --git a/fiz/vaje/4/.gitignore b/fiz/vaje/4/.gitignore
new file mode 100644
index 0000000..4eb278d
--- /dev/null
+++ b/fiz/vaje/4/.gitignore
@@ -0,0 +1 @@
+v_od_x.tsv
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
diff --git a/fiz/vaje/4/nihanje.tsv b/fiz/vaje/4/nihanje.tsv
new file mode 100644
index 0000000..40de805
--- /dev/null
+++ b/fiz/vaje/4/nihanje.tsv
@@ -0,0 +1,1201 @@
+t	x	v	a

+0.05	0.073402	-0.395021667	-0.247764568

+0.1	0.053851	-0.40474	-0.296668534

+0.15	0.033957	-0.422633167	-0.308636481

+0.2	0.0121765	-0.447710278	-0.107282778

+0.25	-0.012348	-0.444851944	0.342385988

+0.3	-0.033614	-0.411123611	0.799687562

+0.35	-0.0533365	-0.369010833	1.321661574

+0.4	-0.0728875	-0.278592222	1.774813272

+0.45	-0.081977	-0.173119722	1.84060787

+0.5	-0.0896945	-0.076698611	1.54805216

+0.55	-0.087808	-0.016483056	1.213838889

+0.6	-0.090552	0.027344722	1.226701389

+0.65	-0.0859215	0.089942222	1.554986265

+0.7	-0.083006	0.180741944	1.895075

+0.75	-0.0698005	0.304793611	1.743318673

+0.8	-0.049735	0.377871667	1.1319

+0.85	-0.0300125	0.409408611	0.600832253

+0.9	-0.0090895	0.432751667	0.152285648

+0.95	0.014406	0.429798056	-0.352104321

+1	0.0355005	0.393306667	-0.779742747

+1.05	0.0536795	0.349097778	-1.150426235

+1.1	0.0715155	0.280021389	-1.519998148

+1.15	0.082663	0.190365	-1.74802963

+1.2	0.0903805	0.099851111	-1.856699228

+1.25	0.092953	0.002763056	-1.8993625

+1.3	0.090552	-0.09261	-1.867232716

+1.35	0.083692	-0.186649167	-1.751787809

+1.4	0.0718585	-0.275638611	-1.474529475

+1.45	0.05488	-0.339474722	-1.082831944

+1.5	0.0368725	-0.379396111	-0.741949228

+1.55	0.01715	-0.415601667	-0.350886883

+1.6	-0.0060025	-0.4210325	0.15435

+1.65	-0.026068	-0.400833611	0.671073148

+1.7	-0.0475055	-0.348430833	1.09532392

+1.75	-0.0608825	-0.287453056	1.41815679

+1.8	-0.0770035	-0.209325278	1.718440586

+1.85	-0.083692	-0.099565278	1.689169136

+1.9	-0.085064	-0.024105278	1.358555247

+1.95	-0.0848925	0.028392778	1.167629167

+2	-0.0821485	0.077556111	1.269417593

+2.05	-0.0780325	0.145679722	1.553133642

+2.1	-0.0691145	0.241719722	1.646982253

+2.15	-0.0536795	0.332328889	1.30641713

+2.2	-0.0337855	0.382254444	0.735120988

+2.25	-0.014063	0.399023333	0.24036466

+2.3	0.006174	0.404263611	-0.210140432

+2.35	0.0276115	0.381015833	-0.676631019

+2.4	0.045619	0.330232778	-1.015714043

+2.45	0.060711	0.272208611	-1.222519753

+2.5	0.072716	0.211040278	-1.458173457

+2.55	0.0828345	0.129673056	-1.723098611

+2.6	0.0866075	0.030488889	-1.824834105

+2.65	0.085407	-0.061644722	-1.750358642

+2.7	0.079919	-0.144822222	-1.635178395

+2.75	0.0708295	-0.223045278	-1.521956636

+2.8	0.057967	-0.303650278	-1.267353241

+2.85	0.0392735	-0.358625556	-0.829181327

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diff --git a/fiz/vaje/4/preseki.py b/fiz/vaje/4/preseki.py
new file mode 100755
index 0000000..7a35c66
--- /dev/null
+++ b/fiz/vaje/4/preseki.py
@@ -0,0 +1,25 @@
+#!/usr/bin/python3
+from sys import stderr
+from math import log
+import numpy
+import csv
+t = []
+x = []
+v = []
+with open("nihanje.tsv") as file:
+	tsv = csv.reader(file, delimiter="\t")
+	i = -1
+	for line in tsv:
+		if i == -1:
+			i = i + 1
+			continue
+		t.append(float(line[0]))
+		x.append(float(line[1]))
+		v.append(float(line[2]))
+		i = i + 1
+zero_crossings_x = numpy.where(numpy.diff(numpy.sign(x)))[0]
+zero_crossings_v = numpy.where(numpy.diff(numpy.sign(v)))[0]
+print("v\tx\tt\tabsx\tln")
+for i in range(len(zero_crossings_x)-1):
+	print(f"{v[zero_crossings_x[i]]}\t{x[zero_crossings_v[i]]}\t{t[zero_crossings_v[i]]}\t{abs(x[zero_crossings_v[i]])}\t{log(abs(x[zero_crossings_v[i]])/0.0943867)}")
+print(f"za {len(zero_crossings_x/2)} nihajev je preteklo {t[zero_crossings_x[len(zero_crossings_x)-1]]-t[zero_crossings_x[0]]} sekund, zato je nihajni čas {(t[zero_crossings_x[len(zero_crossings_x)-1]]-t[zero_crossings_x[0]])/(len(zero_crossings_x)/2)}", file=stderr)