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-rw-r--r--.gitignore2
-rw-r--r--fiz/vaje/3/dokument.lyx1073
-rw-r--r--fiz/vaje/3/meritev.tsv8
-rw-r--r--fiz/vaje/4/.gitignore1
-rw-r--r--fiz/vaje/4/dokument.lyx713
-rw-r--r--fiz/vaje/4/nihanje.tsv1201
-rwxr-xr-xfiz/vaje/4/preseki.py25
7 files changed, 3023 insertions, 0 deletions
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>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
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+\end_layout
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+
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+\begin_inset Text
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+\begin_layout Plain Layout
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+\begin_inset Text
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+\begin_layout Plain Layout
+0,09
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+\begin_layout Plain Layout
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+</cell>
+<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Plain Layout
+620
+\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
+67,58
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\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
+2.9 0.0210945 -0.388638056 -0.333895679
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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)