normal acceleration

The vector acceleration is defined as the following limit:

\[
\mathbf{a} = \lim_{\Delta t \to 0} \frac{\Delta \mathbf{v}}{\Delta t} = \frac{d\mathbf{v}}{dt}
\]

Simple harmonic motion is the projection of uniform circular motion onto a diameter. Its position over time is given by:

\[
x(t) = A \sin(\omega t)
\]