I can't figure out your setup so let's do this. I will show you how to calculate the apparent weight (aka the normal force, aka the scale reading) of an object on a scale under the influence of a sinusoidal wave.
According to Newton's 2nd the normal force on an object under an acceleration is
where m is the mass of the object.
Now, the position of a sinusoidally moving object can be represented as
where A is the amplitude of the wave and is the angular frequency of the wave. (In order to use this formula we must have that and . You can see this from the formulas below. If you can't arrange these conditions then you will need to include a phase angle into the argument of the sine function.)
Thus your normal force (scale reading) as a function of time is: