diff --git a/src/6_bonds_and_spectra_solutions.md b/src/6_bonds_and_spectra_solutions.md index ea7040ce082ee5ce465d8e235069ddbe07c24437..4388a91e2da2c7b541cda0927f79d2c0951e74cf 100644 --- a/src/6_bonds_and_spectra_solutions.md +++ b/src/6_bonds_and_spectra_solutions.md @@ -29,9 +29,9 @@ $$ 1. In 1D, there are two normal modes and in 3D there are 4 normal modes 2. $$ \begin{cases} - m \ddot{x}_1 & = -\kappa(x_1-x_2)\\ - M \ddot{x}_2 & = -\kappa(2x_2-x_1-x_3)\\ - m \ddot{x}_3 & = -\kappa(x_3-x_2) + m \ddot{u}_1 & = -\kappa(u_1-u_2)\\ + M \ddot{u}_2 & = -\kappa(2u_2-u_1-u_3)\\ + m \ddot{u}_3 & = -\kappa(u_3-u_2) \end{cases} $$ Where $m$ is the mass of the oxygen atoms and $M$ the mass of the carbon atom. @@ -39,7 +39,7 @@ Where $m$ is the mass of the oxygen atoms and $M$ the mass of the carbon atom. \omega = \sqrt{\frac{\kappa}{m}} $$ 4. $$ -\frac{x_1}{x_2} = -\frac{M}{2m} +\frac{u_1}{u_2} = -\frac{M}{2m} $$ 5. $$ \omega = \sqrt{\frac{\kappa(2m+M)}{mM}}