From 0a39997c12f0d872413f6f08f16dfd65b191ccdd Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Anton=20Luka=20=C5=A0ijanec?= Date: Thu, 17 Nov 2022 00:21:55 +0100 Subject: fiz/vaje/{3..4} --- fiz/vaje/3/dokument.lyx | 1073 ++++++++++++++++++++++++++++++++++++++++++ fiz/vaje/3/meritev.tsv | 8 + fiz/vaje/4/.gitignore | 1 + fiz/vaje/4/dokument.lyx | 713 ++++++++++++++++++++++++++++ fiz/vaje/4/nihanje.tsv | 1201 +++++++++++++++++++++++++++++++++++++++++++++++ fiz/vaje/4/preseki.py | 25 + 6 files changed, 3021 insertions(+) create mode 100644 fiz/vaje/3/dokument.lyx create mode 100644 fiz/vaje/3/meritev.tsv create mode 100644 fiz/vaje/4/.gitignore create mode 100644 fiz/vaje/4/dokument.lyx create mode 100644 fiz/vaje/4/nihanje.tsv create mode 100755 fiz/vaje/4/preseki.py (limited to 'fiz') 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 + + + + + + + + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $n_{\text{{luknje}}}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $x\text{\left[\si{\centi\meter}\right]}$ +\end_inset + + +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +\begin_inset Formula $s\left[\si{\meter}\right]$ +\end_inset + + +\end_layout + +\end_inset + + +\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 + + +\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 + + + + +\begin_inset Text + +\begin_layout Plain Layout +0 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +0,03 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +0,028 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +190 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +62.13 +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +1 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +0,04 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +0,05 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +260 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +63,765 +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +2 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +0,05 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +0,096 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +340 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +66,708 +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +3 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +0,06 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +0,13 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +400 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +65,4 +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +4 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +0,07 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +0,174 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +470 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +65,867 +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +5 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +0,08 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +0,24 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +540 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +66,2175 +\end_layout + +\end_inset + + + + +\begin_inset Text + +\begin_layout Plain Layout +6 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +0,09 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +0,297 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +620 +\end_layout + +\end_inset + + +\begin_inset Text + +\begin_layout Plain Layout +67,58 +\end_layout + +\end_inset + + + + +\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 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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) -- cgit v1.2.3