stylistic:style_transfer, structural:expansion
Two-dimensional oscillators

In two or three dimensions, harmonic oscillators behave similarly to one dimension. The simplest example of this is an isotropic oscillator, where the restoring force is proportional to the displacement from equilibrium with the same restorative constant in all directions. F → = − k r → {\displaystyle {\vec {F}}=-k{\vec {r}}}

This produces a similar solution, but now there is a different equation for every direction. x (t) = A x cos (ω t − δ x), y (t) = A y cos (ω t − δ y), ⋮ {\displaystyle {\begin{aligned}x(t)&=A_{x}\cos(\omega t-\delta _{x}),\\y(t)&=A_{y}\cos(\omega t-\delta _{y}),\\&\;\,\vdots \end{aligned}}}