Interesting. I've never heard of this before, but according to
wikipedia, simple harmonic motion is given by:
where
is displacement,
is time,
is amplitude,
is frequency, and
is phase.
We also note that period
is given by:
This means that
. So:
To find velocity, we take the derivative:
To find velocity extrema, we take the derivative of
and set it equal to zero:
Let's plug that into our velocity function:
Since the amplitude must be a positive value, we can just say:
Now, the center of oscillation is another way of saying
. So:
Let's let
and
:
And we plug that into our velocity function:
Then plug in
:
But of course we know that speed is relative, and so the value is actually: