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I Need Help Clearing For B On An Equation

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#1 leomarrg

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Posted 26 February 2020 - 04:38 PM

Consider the movement of the mass and spring with friction
A * [e ^ - (b / 2m) t] * cos (sqrt (k / m - (b / 2m) ^ 2)) t + φ)
With A = 2m, k = 3N / m, m = 5Kg and φ = 0, we could change to the value of "b" from zero until the oscillations disappear for the first time and the function does not change to negative values. In this case, the friction now has a very noticeable effect: it lengthens the period of the oscillation so much that no oscillations will be seen (T -> infinity).
The theory indicates when that should happen. Clear for b from the equation and record the predicted value for b = .... (Kg / s) (at least two decimal places to the right of the point)
The question is complete, the exercise is clear for b, I don't get how to do it. The answer is 7.746

Edited by leomarrg, 26 February 2020 - 04:39 PM.


#2 Flummoxed

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Posted 27 February 2020 - 03:50 AM

 

Consider the movement of the mass and spring with friction
A * [e ^ - (b / 2m) t] * cos (sqrt (k / m - (b / 2m) ^ 2)) t + φ)
With A = 2m, k = 3N / m, m = 5Kg and φ = 0, we could change to the value of "b" from zero until the oscillations disappear for the first time and the function does not change to negative values. In this case, the friction now has a very noticeable effect: it lengthens the period of the oscillation so much that no oscillations will be seen (T -> infinity).
The theory indicates when that should happen. Clear for b from the equation and record the predicted value for b = .... (Kg / s) (at least two decimal places to the right of the point)
The question is complete, the exercise is clear for b, I don't get how to do it. The answer is 7.746

 

 

Ive never seen a mass spring damper modeled like this, you may just have part of the equation, or maybe ive forgotten the basics. I think you are going to fail :( 

 

The friction in a system normally damps the oscillation, it does not change its frequency. A quick google however flashes up various worked examples and explanations. To save me correcting your math, here is a quick and easy example https://faculty.wash.../reading-3b.pdf You could try looking at other examples by simply googling spring mass damper examples/systems. Its not rocket science.


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