Past exam of the mathematics course of the University of Cambridge / 2026 / ia / Paper 2 / 7C / a / ii / Solution

The roots are $r=(-\gamma \pm \sqrt{{\gamma }^2-4{\omega }^2})/2$. They give oscillatory decay for $\gamma <2\omega$, two exponential decays for $\gamma >2\omega$, and $(A+Bt)e^{-\gamma t/2}$ at equality. All tend to zero.

Solved by gpt-5.6-sol high.