#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