Update 8_many_atoms_solutions.md

src/8_many_atoms_solutions.md

@@ -134,7 +134,7 @@ The unit cell should contain exactly one spring of $\kappa_1$, $\kappa_2$ and $\
 
 Use the same procedure as before to find: 
 
-$$ m \begin{pmatrix} u_{1,n} \\ u_{2,n} \\ u_{3,n} \end{pmatrix} = \begin{pmatrix} -\kappa_1(u_{n,2}-u_{n,1}) -\kappa_3(u_{n-1,3}-u_{n,1}) \\ -\kappa_2(u_{n,3}-u_{n,2}) -\kappa_1(u_{n,3}-u_{n,2}) \\ -\kappa_3(u_{n+1,1}-u_{n,3}) -\kappa_2(u_{n,2}-u_{n,3}) \end{pmatrix} $$
+$$ m \begin{pmatrix} \ddot{u}_{1,n} \\ \ddot{u}_{2,n} \\ \ddot{u}_{3,n} \end{pmatrix} = \begin{pmatrix} \kappa_1(u_{n,2}-u_{n,1}) + \kappa_3(u_{n-1,3}-u_{n,1}) \\ +\kappa_2(u_{n,3}-u_{n,2}) +\kappa_1(u_{n,3}-u_{n,2}) \\ \kappa_3(u_{n+1,1}-u_{n,3}) + \kappa_2(u_{n,2}-u_{n,3}) \end{pmatrix} $$
 
 ### Subquestion 3