Past exam of the mathematics course of the University of Cambridge / 2018 / iii / Paper 331 / 1 / b / ii / Solution

For the growing normal mode in two deep layers,It vanishes at the endpoints of the unstable band and has its unique interior maximum where $A-3\gamma k^2=0$. Using $k_c=\sqrt{A/\gamma }$ givesThis is the maximum exponential growth rate, not the real oscillation frequency.