\begin{tikzpicture}[thick,scale=0.35]
% Define positions of the 10 circles in a ring-like arrangement
\coordinate (A) at (3,0);
\coordinate (B) at (2.6, 1.8);
\coordinate (C) at (1.8, 2.6);
\coordinate (D) at (0,3);
\coordinate (E) at (-1.8, 2.6);
\coordinate (F) at (-2.6, 1.8);
\coordinate (G) at (-3,0);
\coordinate (H) at (-2.6,-1.8);
\coordinate (I) at (-1.8,-2.6);
\coordinate (J) at (0,-3);
% Draw circles
\fill[black] (A) circle (0.2);
\fill[black] (B) circle (0.2);
\fill[black] (C) circle (0.2);
\fill[black] (D) circle (0.2);
\fill[black] (E) circle (0.2);
\fill[black] (F) circle (0.2);
\fill[black] (G) circle (0.2);
\fill[black] (H) circle (0.2);
\fill[black] (I) circle (0.2);
\fill[black] (J) circle (0.2);
% Add labels
\node[xshift=3mm] at (A) {$x_1$};
\node[xshift=3mm] at (B) {$x_2$};
\node[xshift=1.8mm, yshift=1.8mm] at (C) {$x_3$};
\node[yshift=2.6mm] at (D) {$x_4$};
\node[yshift=2.8mm] at (E) {$x_5$};
\node[xshift=-2mm, yshift=1.8mm] at (F) {$x_6$};
\node[xshift=-3mm] at (G) {$x_7$};
\node[xshift=-1.8mm, yshift=-1.8mm] at (H) {$x_8$};
\node[xshift=-1.8mm, yshift=-1.8mm] at (I) {$x_9$};
\node[yshift=-2.6mm] at (J) {$x_{10}$};
% Draw springs between adjacent circles
\draw[decorate, decoration={coil, aspect=0.5, segment length=1.2mm, amplitude=1mm}] (A) -- (B);
\draw[decorate, decoration={coil, aspect=0.5, segment length=1.2mm, amplitude=1mm}] (B) -- (C);
\draw[decorate, decoration={coil, aspect=0.5, segment length=1.2mm, amplitude=1mm}] (C) -- (D);
\draw[decorate, decoration={coil, aspect=0.5, segment length=1.2mm, amplitude=1mm}] (D) -- (E);
\draw[decorate, decoration={coil, aspect=0.5, segment length=1.2mm, amplitude=1mm}] (E) -- (F);
\draw[decorate, decoration={coil, aspect=0.5, segment length=1.2mm, amplitude=1mm}] (F) -- (G);
\draw[decorate, decoration={coil, aspect=0.5, segment length=1.2mm, amplitude=1mm}] (G) -- (H);
\draw[decorate, decoration={coil, aspect=0.5, segment length=1.2mm, amplitude=1mm}] (H) -- (I);
\draw[decorate, decoration={coil, aspect=0.5, segment length=1.2mm, amplitude=1mm}] (I) -- (J);
\draw[decorate, decoration={coil, aspect=0.5, segment length=1.2mm, amplitude=1mm}] (J) -- (A); % Connect last to first
\end{tikzpicture}