Made DOS exercise in ex. 1 simpler

src/8_many_atoms.md

@@ -229,8 +229,7 @@ Recall the eigenfrequencies of a diatomic vibrating chain in the lecture notes w
 
 1. Find the magnitude of the group velocity near $k=0$ for the _acoustic_ branch.
 2. Show that the group velocity at $k=0$ for the _optical_ branch is zero.
-3. Derive an expression for the density of states $g(\omega)$ in the _optical_ branch.
-4. Make a plot of your expression of $g(\omega)$ found in 3. Does the plot look like the bar diagram of the density of states of the optical branch in the lecture notes?
+3. Derive an expression for the density of states $g(\omega)$ for the _acoustic_ branch and small $ka$. Make use of your expression of the group velocity in 1.
 
 #### Exercise 2: atomic chain with 3 different spring constants
 Suppose we have a vibrating 1D atomic chain with 3 different spring constants alternating like $\kappa_ 1$, $\kappa_2$, $\kappa_3$, $\kappa_1$, etc. All the the atoms in the chain have an equal mass $m$.