 Solution

ID: past-exam-of-the-short-options-paper-shared-by-prelims-and-parts-a-and-b-of-the-physics-course-of-the-university-of-oxford/2017/s7/2/b/solution

Differentiate the quadratic Lagrangian with respect to coordinates and velocities. The equations are

\overset{x}{¨}_{1} - 2Ω \overset{x}{˙}_{2} + (2 k^{'} / m - Ω^{2}) x_{1} = 0, \overset{x}{¨}_{2} + 2Ω \overset{x}{˙}_{1} + (2 k / m - Ω^{2}) x_{2} = 0.

- Ω^{2} x_{i}

to the force side identifies the outward centrifugal acceleration. The remaining terms are elastic restoring forces. The sign pair is fixed by the rotating-basis convention in part a.

 New to topics? Read the docs here!