https://en.wikipedia.org/wiki/ResonanceWith the simple Harbor Freight class of vibratory tumbler
there is probably an “Optimum Shake Mass”
where vibration stroke is highest because it is near resonant frequency.
The input frequency is the speed of vibrator motor (assuming it drives one single crank weight)
and needs to converted to units of Hertz, cycles per second.
3600 rpm is cycles per minute and should be converted to cycles per second so
3600/60 = 60 Hertz
1800 rpm would be 30 Hertz,
etc
Spring rate is calculated similar to engine valve spring rate measurement
but needs to be in units of Newtons per Meter
instead of LBS per inch.
Be careful if you choose to use “American” style units of LBS
because a “Pound” is a unit of Force, not a mass.
You have to know when to
divide Pounds by 32.2 feet per second per second, the acceleration of Gravity in the American units system
to convert to the seldom heard of “Poundals” of mass for use in math equations.
If you did not go to Engineering School prior to year 1980 you will probably make a mistake.
Stick with kilograms, meters and seconds.
Just as an example,
Let us say the motor is 1800 rpm, (30 Hertz)
The bowl and lid of the vibratory polisher weighs 250 grams.
If you add 750 grams of parts to this 250 gram bowel, the springs beneath compress 2 mm.
K the Spring Rate is (.250 KG + .750 KG) divided by ( 2/1000 meters)
( 1 KG divided by 0.002 meters)
= 500 KG per Meter
The simple Resonance equation is
Omega = SQUARE ROOT [K/M ]
30 Hertz = SR [ 500/ M]
30 x 30 = 500/M
900 = 500 /M
M = 500/900
Mass that creates resonance is 0.555 of a Kilogram
This is the mass of the parts plus bowl
Subtract the .250 KG mass of the bowl to find the mass of parts
only 305 grams of the sum of media plus parts can be cleaned at maximum shake.
The above numbers are just guesses for example of the math.
Each vibratory cleaner spring rate, masses and true operating rpm of motor under load would have to be measured by its owner.
