
\magnification=\magstep1


$$
y(t) \quad = \quad A \cos( \omega t + \phi )
$$

$$
\eqalign{
v(t) \quad &= \quad {{ dy} \over {dt} } \cr
           &\phantom{=} \cr
           &= \quad - \omega A \sin( \omega t + \phi )  \cr
}
$$


$$
\eqalign{
a(t) \quad &= \quad {{ dv} \over {dt} } \cr
           &\phantom{=} \cr
           &= \quad - \omega^2 A \cos( \omega t + \phi )  \cr
}
$$


$$
{\rm KE\ } \quad  = \quad {{1}\over{2}} m v^2
$$

$$
{\rm KE\ } \quad  = \quad {{1}\over{2}} m \omega^2 A^2 \sin^2(\omega t + \phi)
$$


$$
\eqalign{
{\rm PE\ } \quad &= \quad {{1}\over{2}} k (y - y_{eq})^2  \cr
           & \cr
                 &= \quad {{1}\over{2}} k y^2 \qquad \qquad , {\rm\ \  if\ we\ choose\ } y_{eq} = 0 \cr
}
$$

$$
{\rm PE\ } \quad  = \quad {{1}\over{2}} k A^2 \cos^2(\omega t + \phi)
$$


\bye
