# Need help to arrive at a formula/equation

1. Jul 7, 2004

### malzki

Hello everybody!
I hope you could help me with my problem.
I am trying to simulate a program for a scale that measures the weight of liquids in a bottle or in a container.
After placing the container in the scale, i need to get an estimated weight (with accuracy of -5% to +5%) within 500 ms.
Placing the container on the scale generates vibration and weight is unstable for the first few seconds.
Do you have any idea how can i get an estimated weight of the object that i placed on the scale?
I think this is related and somewhat similar to spring equations but i don't know exactly what equation or solution to use.
I appreciate any help that you can give.

malzki

2. Jul 7, 2004

### AKG

Assume that the scale acts as a spring, and for the first few seconds, the object placed on the scale undergoes simple harmonic motion. At this point, if what I've said doesn't help, then I'd need more information. What kind of readings do you know about the scale. If you wanted, could you get the spring co-efficient for the scale? What other information do you have at your disposal, so far I don't think there's enough information to answer your question.

3. Jul 7, 2004

### Wong

Just curious...why should one want to take the reading of the weight when the reading on the scale is unstable? Why not wait until the reading gets stable? I think for a good scale there should be enough "damping" such that the reading gets stable very quickly?

Or rather would you want to use "simple harmonic motion" to estimate the inertial mass of a liquid? (i.e. attach a spring to the cup of liquid and set it into motion and take some readings)

4. Jul 7, 2004

### malzki

Yes, this is similar to what i want to do.
By the way, it seems that my problem is vibration and other factors that affect the weight of some objects on a scale. And this is especially for objects that i need to weigh precisely (example, my scale is graduated in 0.01 gram).
I also appreciate if you can suggest me solutions to lessen the effect of vibration.

5. Jul 7, 2004

### enigma

Staff Emeritus
Get a really heavy scale.

6. Jul 17, 2004

### rayjohn01

Someone mentioned damping, and I would suggest if this is a theoretical experiment that you think of that, the mass starts with potential energy which unless lossed by some mechanism would keep an idealised scale moving forever. Natural scales have losses but they may not be enough , the solution is to create 'critical' damping where the mass moves smoothly with a very small overshoot -- there is a maths expression for such but I cannot remember what it is. Ray
In this scenario the first overshoot( and there is only one ) is equal to your error allowance.
I remember now it's a simple Bessel expression for simple harmonic motion with critical damping ( assumes small deviations hence linear) you need to develop an equation of motion in which a force exists dependant upon velocity
obviously this disappears when the mass comes to rest, and is largest as the mass is accellerated to it's greatest speed. IT's equivalent to a term involving dx/dt in the diff equation d^2(x)/dt^2 + k dx/dt + a =0 , if k=0 the system is undamped and results in sinusoidal motions.

Last edited: Jul 17, 2004
7. Jul 19, 2004