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% Document Info
\author{bsmith}
\pdfinfo{
  /Title (vibrations-rappel.pdf)
  /Creator (Cheatography)
  /Author (bsmith)
  /Subject (Vibrations Rappel Cheat Sheet)
}

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\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
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    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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\columnbreak
\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Vibrations Rappel Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{bsmith} via \textcolor{DarkBackground}{\uline{cheatography.com/129311/cs/25555/}}}
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\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{LL}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}bsmith \\
  \uline{cheatography.com/bsmith} \\
  \end{tabulary}
\vfill
\columnbreak
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  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Not Yet Published.\\
   Updated 16th February, 2021.\\
   Page {\thepage} of \pageref{LastPage}.
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  \vspace{-5pt}
  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
\end{tabulary}
\end{multicols}}




\begin{document}
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\begin{multicols*}{4}

\begin{tabularx}{3.833cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Mouvements Périodiques}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{3.833cm}}{Mouvements périodiques =\textgreater{} Mouvements sinusoïdales x=Acos(wt+α)} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{Forme équation de mouvement : d$^{\textrm{2}}$x/dt$^{\textrm{2}}$ + w$^{\textrm{2}}$x=0 avec w=√(k/m)} \tn 
% Row Count 4 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{3.833cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Superposition}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{3.833cm}}{Fréquences égales : x = A cos(wt+φ) avec : A$^{\textrm{2}}$=(A1)$^{\textrm{2}}$+(A2)$^{\textrm{2}}$+2(A1)(A2)cos(φ2-φ1) et tg φ = (A1sinφ1 + A2sinφ2)/(A1cosφ1 + A2cosφ2)} \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{Battements : A1≠A2 \& f1≠f2 mais proches: f = | (w1-w2)/2π | = | f1 - f2 |} \tn 
% Row Count 5 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{3.833cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Oscillations libres}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{3.833cm}}{Eq diff du mvt : (1) d$^{\textrm{2}}$x/dt$^{\textrm{2}}$ + w$^{\textrm{2}}$x=0 \#Newton (2) E=1/2 m(dx/dt)$^{\textrm{2}}$ + 1/2 kx$^{\textrm{2}}$ \#Energie} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{MHS rectiligne = résultantes de 2 mvts circulaires réels et opposés de même module} \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{3.833cm}}{Courbe de Lissajous = mvt de 2 oscillations de même amplitude, rectilignes et perpendiculaires} \tn 
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% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{Objets flottants : md$^{\textrm{2}}$y/dt$^{\textrm{2}}$ = -ρgAy avec A:aire section droite de l'objet, y: déplacement =\textgreater{}w=√(ρgA/m)} \tn 
% Row Count 9 (+ 3)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{3.833cm}}{Pendule : E = 1/2 m (dx/dt)$^{\textrm{2}}$ + (mg/2l)y$^{\textrm{2}}$ =\textgreater{} w=√(g/l)} \tn 
% Row Count 11 (+ 2)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{Tube en U : E = 1/2 ρAl(dy/dt)$^{\textrm{2}}$ + gρAy$^{\textrm{2}}$ =\textgreater{} w$^{\textrm{2}}$=2g/l avec A: aire, l: long. tot. liquide, y: position surface du liquide \% position d'équilibre} \tn 
% Row Count 14 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{3.833cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{MHS amorti}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{3.833cm}}{Force de frottements visqueux : F = -bv avec b=coeff de frottement} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{Eq diff du mvt : md$^{\textrm{2}}$x/dt$^{\textrm{2}}$ + bdx/dt +kx=0 =\textgreater{} d$^{\textrm{2}}$x/dt$^{\textrm{2}}$ + b/m dx/dt + k/m x =0 =\textgreater{} wo$^{\textrm{2}}$=k/m ; γ=b/m =\textgreater{} pour tout le système : w = √(wo$^{\textrm{2}}$ - γ$^{\textrm{2}}$/4)} \tn 
% Row Count 5 (+ 3)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{3.833cm}}{Facteur de qlté : Q = wo/γ} \tn 
% Row Count 6 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{Amplitude après n cycles : A(n) = Ao e\textasciicircum{}-nγ/2\textasciicircum{}} \tn 
% Row Count 7 (+ 1)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{3.833cm}}{Rapport des amplitudes après n cycles : An/Ao = exp(nπ/Q)} \tn 
% Row Count 9 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{3.833cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Oscillateurs couplés et modes normaux}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{3.833cm}}{1) Sys. d'eq. diff.\{\{nl\}\}2) Sol forme xn=Ane\textasciicircum{}jwt\textasciicircum{} `(initialement au repos)` xn=Ane\textasciicircum{}j(wt+αxn)\textasciicircum{} `(initialement en mouvement)`\{\{nl\}\}3)Sys. d'eq.\{\{nl\}\}4)Div par me\textasciicircum{}jwt\textasciicircum{}-\textgreater{}Matrice mode normaux\{\{nl\}\}5){[}wo$^{\textrm{2}}$,ws$^{\textrm{2}}$,w$^{\textrm{2}}${]}{[}A,B...{]}={[}0...0{]}\{\{nl\}\}6)Echelonner ou faire ▲=0 pour trouver w} \tn 
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\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{3.833cm}}{N.B. Prendre en compte la tension lors des calculs}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{3.833cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Ondes transversales}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{3.833cm}}{Hypothèses : Fil uniforme de densité linéique 𝜌, Gravité négligeable, T tension constante dans le fil} \tn 
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% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{Equations d'onde : ∂$^{\textrm{2}}$y/∂x$^{\textrm{2}}$=(1/c$^{\textrm{2}}$)(∂$^{\textrm{2}}$y/∂t$^{\textrm{2}}$) \{\{nl\}\}=\textgreater{}Sol y=a sin(ω t -Φ)=a sin{[}2π/λ(ct-x){]} \{\{nl\}\} 2πc/λ=ω=2πv et Φ=2πx/λ\{\{nl\}\}c=λv} \tn 
% Row Count 7 (+ 4)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{3.833cm}}{Période des oscillations : λ /c=1/v=τ avec λ:long. d'onde} \tn 
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% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{ct-x =\textgreater{} depl. vers la droite ct+x =\textgreater{} depl. vers la gauche} \tn 
% Row Count 11 (+ 2)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{3.833cm}}{Expressions équivalentes : y=a sin{[}(2π/λ)(ct-x)=a sin 2π(vt-x/λ)=a sin ω(t-x/c)=a sin(ωt-kx)} \tn 
% Row Count 13 (+ 2)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{Vitesse de phase ou vitesse d'onde :∂x/∂t} \tn 
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% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{3.833cm}}{Vitesse d'un oscillateur : ∂y/∂t} \tn 
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% Row 7
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{Impédance : Z=Force transversale/vitesse transversale \{\{nl\}\}= F/v avec F=-T(∂y/∂x)} \tn 
% Row Count 17 (+ 2)
% Row 8
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{3.833cm}}{\seqsplit{∂y/∂t=(-ω/k)(∂y/∂x)=(-∂x/∂t)(∂y/∂x)=-c∂y/∂x}} \tn 
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% Row 9
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{Déplacement de l'onde : {\bf{y}}={\bf{A}}e\textasciicircum{}j(ωt-kx)\textasciicircum{}} \tn 
% Row Count 20 (+ 1)
% Row 10
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{3.833cm}}{Impédance : Z=Force transversale/vitesse transversale \{\{nl\}\}= F/v avec F=-T(∂y/∂x)=jkT{\bf{A}}e\textasciicircum{}j(ωt-kx)\textasciicircum{}} \tn 
% Row Count 23 (+ 3)
% Row 11
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{{\bf{A}}=Fo/jkT=Fo/jω(c/T)} \tn 
% Row Count 24 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{3.833cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Oscillations forcées et résonance}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{3.833cm}}{Mvt syst. = combinaison des oscillations de fréquences ω0 (fréquence naturelle) et ω (fréquence force)} \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{Intervalle de temps où les 2 types de vibration sont présentes = régime transitoire} \tn 
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% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{3.833cm}}{Oscillations forcées seules présentes = régime permanent} \tn 
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% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{Amplitude max =\textgreater{} ωo = ω} \tn 
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% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{3.833cm}}{Oscillateur forcé non amorti : md\textasciicircum{}2\textasciicircum{}x/dt\textasciicircum{}2\textasciicircum{} + kx = F0cosωt} \tn 
% Row Count 10 (+ 2)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{Oscillations forcées avec amortissement : d$^{\textrm{2}}$x/dt$^{\textrm{2}}$ + ɣ dx/dt + ωo$^{\textrm{2}}$ x = Fo/m cosωt} \tn 
% Row Count 12 (+ 2)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{3.833cm}}{1. Trouver eq de forme : md\textasciicircum{}2\textasciicircum{}x/dt\textasciicircum{}2\textasciicircum{} + kx = F0cos ωt \{\{nl\}\} 2. Solution : z=A e\textasciicircum{}j(ωt+α)\textasciicircum{}`(non amorti)` z =Ae\textasciicircum{}j(ωt-α)\textasciicircum{}`(amorti)`\{\{nl\}\}3. Regrouper termes semblables\{\{nl\}\}4. Décomposer e\textasciicircum{}ix\textasciicircum{} = cos x + i sin x \{\{nl\}\}5. Système d'eq par identification\{\{nl\}\}6. Résoudre pour A `(élever au carré,addition) et tg=sin/cos`} \tn 
% Row Count 19 (+ 7)
% Row 7
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{Fréquence max : ωm = ωo(1- 1/(2Q$^{\textrm{2}}$))\textasciicircum{}1/2\textasciicircum{}} \tn 
% Row Count 20 (+ 1)
% Row 8
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{3.833cm}}{Amplitude max : Am = Ao Q/(1- 1/(4Q$^{\textrm{2}}$))\textasciicircum{}1/2\textasciicircum{}} \tn 
% Row Count 21 (+ 1)
% Row 9
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{P = dW/dt = F dx/dt = Fv avec F = F0 cos ωt et x= (Fo/m)cos(ωt)  / (ωo$^{\textrm{2}}$-ω$^{\textrm{2}}$) = C cos ωt (non amorti) ou x=A cos(ωt – δ) (amorti)} \tn 
% Row Count 24 (+ 3)
% Row 10
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{3.833cm}}{Vitesse max =\textgreater{} ω = ω0 = résonnance de vitesse.} \tn 
% Row Count 25 (+ 1)
% Row 11
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{Puissance moyenne : P(ω) = (Fo$^{\textrm{2}}$ωo/2kQ)*{[}1/((ωo/ω - ω/ωo)$^{\textrm{2}}$+1/Q$^{\textrm{2}}$){]}} \tn 
% Row Count 27 (+ 2)
% Row 12
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{3.833cm}}{Puissance maximale : ω=ωo =\textgreater{} Pm = Fo$^{\textrm{2}}$ωoQ/2k ou QFo$^{\textrm{2}}$/2mωo} \tn 
% Row Count 29 (+ 2)
% Row 13
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{ɣ=2▲ω=ωo/Q} \tn 
% Row Count 30 (+ 1)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{3.833cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Oscillations forcées et résonance (cont)}}  \tn
% Row 14
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{3.833cm}}{E=Eoe\textasciicircum{}-ɣt\textasciicircum{}} \tn 
% Row Count 1 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{3.833cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Equation de d'Alembert-Lagrange}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{3.833cm}}{Equation de Lagrange : d/dt(∂L/∂q'j) - ∂L/∂qj + ∂R/∂q'j = Qj  (horizontal : qj=xj, vertical: qj=yj)} \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{L = T -V avec T = ∑1/2 mα(vα)\textasciicircum{}2\textasciicircum{} et V=∑(Fi)(ri)} \tn 
% Row Count 5 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{3.833cm}}{Trouver l'équ. diff. du mvt à partir de l'éq. de Lagrange\{\{nl\}\}1. Chercher T et V pour trouver L. \{\{nl\}\}2. R = 0 (pas de frottement proportionnel à la vitesse) et Qj = 0 (pas de forces non conservatives)\{\{nl\}\}3. Plug in it epi lapè.} \tn 
% Row Count 10 (+ 5)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{Trouver les modes normaux : Après avoir trouvé le syst. d'éq. diff., on met sous forme matricielle 𝐌𝐱" +𝐊𝐱=𝟎 et on résoud en prenant des solutions de la forme 𝐱(t)= {[}X1e\textasciicircum{}st\textasciicircum{} X2e\textasciicircum{}st\textasciicircum{}{]} On doit résoudre 𝐝𝐞𝐭( (𝐌\textasciicircum{}−1\textasciicircum{}𝐊) −λ𝐈 )=𝟎 pour trouver les valeurs propres λ. Ce qui donne des solutions de la forme 𝐱= 𝛟re\textasciicircum{}±jωrt\textasciicircum{} avec ωr= (λr)\textasciicircum{}1/2\textasciicircum{} et 𝛟r={[}a b{]} lorsqu'on resoud ( (𝐌\textasciicircum{}−1\textasciicircum{}𝐊) −λ𝐈 ){[}a b{]}={[}0 0{]}} \tn 
% Row Count 20 (+ 10)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{3.833cm}{x{1.7165 cm} x{1.7165 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{3.833cm}}{\bf\textcolor{white}{Formulaire de Trigonométrie}}  \tn
% Row 0
\SetRowColor{LightBackground}
cos(x + 2π) = cos x & sin(x + 2π) = sin x \tn 
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% Row 1
\SetRowColor{white}
cos(x + π) = − cos x & sin(x + π) = − sin x \tn 
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% Row 2
\SetRowColor{LightBackground}
cos(π/2 - x) = sin x & sin(π/2 - x) = cos x \tn 
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% Row 3
\SetRowColor{white}
cos(π/2 + x) = - sin x & sin(π/2 + x) = cos x \tn 
% Row Count 7 (+ 2)
% Row 4
\SetRowColor{LightBackground}
cos(a + b) = cos a cos b − sin a sin b & sin(a + b) = sin a cos b + sin b cos a \tn 
% Row Count 9 (+ 2)
% Row 5
\SetRowColor{white}
cos(a − b) = cos a cos b + sin a sin b & sin(a − b) = sin a cos b − sin b cos a \tn 
% Row Count 12 (+ 3)
% Row 6
\SetRowColor{LightBackground}
cos(2a) = cos\textasciicircum{}2\textasciicircum{} a − sin\textasciicircum{}2\textasciicircum{} a & sin(2a) = 2 sin a cos a \tn 
% Row Count 14 (+ 2)
% Row 7
\SetRowColor{white}
cos a cos b = 1/2 (cos(a − b) + cos(a + b)) & sin a sin b = 1/2 (cos(a + b) - cos(a - b)) \tn 
% Row Count 17 (+ 3)
% Row 8
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{3.833cm}}{sin a cos b =1/2 (sin(a + b) + sin(a − b))} \tn 
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% Row 9
\SetRowColor{white}
cos\textasciicircum{}2\textasciicircum{} a =1/2 (1 + cos(2a)) & sin\textasciicircum{}2\textasciicircum{} a =1/2 (1 − cos(2a)) \tn 
% Row Count 20 (+ 2)
% Row 10
\SetRowColor{LightBackground}
cos p + cos q = 2 \seqsplit{cos((p+q)/2)cos((p-q)/2)} & sin p + sin q = 2 \seqsplit{sin((p+q)/2)cos((p-q)/2)} \tn 
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% Row 11
\SetRowColor{white}
cos p - cos q = - 2 \seqsplit{cos((p+q)/2)cos((p-q)/2)} & sin p - sin q = -2 \seqsplit{cos((p+q)/2)sin((p-q)/2)} \tn 
% Row Count 26 (+ 3)
% Row 12
\SetRowColor{LightBackground}
1 + cos x = 2 cos\textasciicircum{}2\textasciicircum{}x/2 & 1 − cos x = 2 sin\textasciicircum{}2\textasciicircum{}x/2 \tn 
% Row Count 28 (+ 2)
% Row 13
\SetRowColor{white}
cos x = cos a ⇔ x = a + 2kπ ou x = -a + 2kπ & sin x = sin a ⇔ x = a + 2kπ ou x = π − a + 2kπ \tn 
% Row Count 31 (+ 3)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{3.833cm}{x{1.7165 cm} x{1.7165 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{3.833cm}}{\bf\textcolor{white}{Formulaire de Trigonométrie (cont)}}  \tn
% Row 14
\SetRowColor{LightBackground}
e\textasciicircum{}ix\textasciicircum{} + e\textasciicircum{}−ix\textasciicircum{} = 2 cos x & e\textasciicircum{}ix\textasciicircum{} − e\textasciicircum{}−ix\textasciicircum{} = 2i sin x \tn 
% Row Count 2 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}