Past exam of the MPhil in nuclear energy course of the University of Cambridge / 2021 / Module NE1 / 2 / d / Solution

Multiply the supplied inhour equation by $\omega +\lambda$ and collect powers of the inverse period:With the stipulated constants this becomeswith roots ${\omega }_{+}=0.0165064{\mathrm{s}}^{-1}$ and ${\omega }_{-}=-12.1165{\mathrm{s}}^{-1}$. The negative root describes a rapidly decaying component. The positive root governs the late-time growth, givingThe growing-mode e-folding time is not the precursor mean lifetime, and the negative root is a legitimate transient mode rather than an unphysical negative time.