Changes between Version 4 and Version 5 of u/erica/JeansInstability
 Timestamp:
 06/20/13 20:17:09 (11 years ago)
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u/erica/JeansInstability
v4 v5 33 33 [[latex($\rho_1 = \cos(kx)e^{^+ _\omega t}$)]] 34 34 35 Thus, the perturbation takes on a form that is oscillatory in x and exponential in time. What we'd like to do now is determine, for which frequencies is the perturbation ''unstable'' (exponentially growing), and for what frequencies is the perturbation ''stable'' (exponentially decaying). In order to determine this we can rewrite [[latex($\omega$)]] asa more intuitive form.35 Thus, the perturbation takes on a form that is oscillatory in x and exponential in time. What we'd like to do now is determine, for which frequencies is the perturbation ''unstable'' (exponentially growing), and for what frequencies is the perturbation ''stable'' (exponentially decaying). In order to determine this we can rewrite [[latex($\omega$)]] into a more intuitive form. 36 36 37 37