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+#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