An easy start: springs
$\vec{F}= -k(x-x_0)\vec{u}_x$
$\vec{F}=m\vec{a}$
$-k(x-x_0)\vec{u}_x = m\ddot{x}\vec{u}_x$
$\ddot{x}=-\frac{k}{m}(x-x_0)$
$\vec{F}= -k(x-x_0)\vec{u}_x$
$\vec{F}=m\vec{a}$
$-k(x-x_0)\vec{u}_x = m\ddot{x}\vec{u}_x$
$\ddot{x}=-\frac{k}{m}(x-x_0)$