1. Consider a particle of mass $m$ moving vertically in a fluid with quadratic drag force $Dv^2$, where $v$ is its velocity and $D > 0$ is a constant. The particle is also acted on by gravity, with acceleration due to gravity $g$.
  2. A particle of mass $m$ moves along the $x$ axis with one end attached to a spring of spring constant $k > 0$, and is subjected to an additional force $F_0\cos Ωt$.
  3. Consider a particle of charge $q$ moving in a constant electromagnetic field. Without loss of generality we take the magnetic field $\mathbf B = (0, 0, B) ≠ 0$ to point along the $z$ axis, while
    the electric field $\mathbf E = (E_1, E_2, E_3)$ is constant, but arbitrary.
  4. Consider a particle of mass $m$ moving in a plane with position vector $\mathbf r = (x, y)$, subject to a force $\mathbf F = -k\mathbf r$, where $k > 0$ is constant.