Past exam of the physics course of the year 1 of the natural sciences course of the University of Cambridge / 2021 / Section B / 8 / f / Solution

The parameters giveThe coordinate expressions for the initially circular damped planar oscillator areThe damped oscillation period $2\pi /\nu =1.00052\mathrm{s}$ gives almost four anticlockwise turns in four seconds. The radius envelope falls by $e^{-\gamma (4\mathrm{s})}=e^{-1}=0.3679$. Substitution into the exact coordinates givesThe left panel annotates the initial tangent, time marks and endpoint. Because $c$ is an unspecified starting coordinate, the axes are normalized by $c$ rather than assigned numerical lengths.