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JeansInstability

-              v2
+              v3
 [[latex($\omega ^2 = C_s^2 k^2 - 4 \pi G \rho_0$)]]
+When
+[[latex($\omega^2 < 0$)]]
+or
+[[latex($4 \pi G \rho_0 > C_s^2 k^2 $)]]
+we see that [[latex($\omega$)]] is imaginary. This implies that there is an exponential growth or decay factor multiplying the oscillatory [[latex($e^{i(\vec{k}\cdot \vec{x})}$)]] in the solution for [[latex($\rho_1$)]]. That is,
+[[latex($\rho_1 = e^{i(\vec{k} \cdot \vec{x})} e^{-i(^+_- i \omega t)} =$)]]
+[[latex($ e^{i(\vec{k} \cdot \vec{x})} e^{^+_-  \omega t}$)]]
+Taking the real part, we have:
+[[latex($\rho_1 = \cos(kx)e^{\omega t}$)]]
+Now, we can rewrite [[latex($\omega$)]] into a more intuitive form.