Help I'm in a real-life physics jam

[johnnyd99]

Homework Statement

I hope I am posting in the right area and you guys can help me out. I'm by no means a physics master but have a basic math understanding. Here is the situation I am dealing with at work:

I am building a vibration table (that goes up and down, 900r/min, with a vertical displacement of 0.33") and it needs to have a minimum acceleration of four times gravitational acceleration.

Basically my set up includes a motor (which I can set to 900r/min) that drives a camshaft that moves the table up. The table floats in between compression springs (four on top, four on bottom).

How do I set and measure the gravitational acceleration on this? I'm assuming I could adjust the gravitational acceleration by adjusting the amount of spring compression...??

If anyone has ideas how I can measure and configure gravitational acceleration on this vibration table it would be of much help!

Thanks!
John

Homework Equations

The Attempt at a Solution

Homework Statement

Homework Equations

The Attempt at a Solution

 

[zhermes]

Well, generally you would use an accelerometer.
Otherwise you can calculate the average acceleration very easily based on the parameters you've given.

More exotic options include (but are not limited to):
- Calculating the force exerted by the motor, and that of the springs
- Using lasers (always works)
- Using magnetics and measuring the electric field
- Use a high speed camera and calculate it for small timesteps manually

 

[Dickfore]

The formula for the maximum acceleration in a harmonic motion is:
$$a_{\mathrm{max}} = \omega^2 \, A$$
where $\omega = 2 \, \pi \, f$ is the circular frequency ($f$ is the regular frequency, in your case 900 r/min), and $A$ is the amplitude.

You need to be careful in converting the units.

 

[johnnyd99]

Thanks for the feedback guys. I'd like to try solving this with a formula if possible, however a lot of this is going over my head >) I'm just reading that I might need to consider something called Hooke's Law? The spring constant (K) is 2.680lbF/in, if this information is needed.

Any chance someone can try solving this based on the data given?

Thanks a bunch

 

[zhermes]

This is your problem, you should solve it. @Dickfore's answer is the best if you have an appropriate geometry between your motor and camshaft (which I'd guess you do). How does the motor's motion get translated to the table motion, exactly?