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pwilmink1-Visitor
1-Visitor
Jul 22, 2014 3:45 PM UTC
Solved

sum several sin

Hi All,

I have a problem. Here I discribe the case.

A triplex plunger pump will produce water hammer. This will create a sinus wave, by opening the inletvalve and closing the inletvalve. I have 3 plunjers so 6 vibration sinus.

I like to sum these sinus. See my enclosed worksheet.

by calculating with my hand calculator I get an answer. In mathcad I get only 'zero' (0). What do I wrong.

Fred_KohlheppAnswer
23-Emerald I
Jul 22, 2014 4:28 PM UTC

Your sheet is correct. Mathcad has tolerances for numbers close to zero being displayed as zero. If you change these values (format/results/tolerances, you get very small numbers. If you calculate y for various values of alpha, you can see that the summation is always very small.

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10 replies

RichardJ19-Tanzanite
19-Tanzanite
Jul 22, 2014 4:25 PM UTC

Terms 1, 2, and 3 sum to zero. So do terms 4, 5, and 6. This is true for all values of alpha, alpha2, and beta.

sumtozero.png

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Fred_Kohlhepp23-Emerald IAnswer
23-Emerald I
Jul 22, 2014 4:28 PM UTC

Your sheet is correct. Mathcad has tolerances for numbers close to zero being displayed as zero. If you change these values (format/results/tolerances, you get very small numbers. If you calculate y for various values of alpha, you can see that the summation is always very small.

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Werner_E
Werner_E25-Diamond I
25-Diamond I
Jul 22, 2014 4:52 PM UTC

Fred Kohlhepp wrote:

Your sheet is correct. Mathcad has tolerances for numbers close to zero being displayed as zero. If you change these values (format/results/tolerances, you get very small numbers. If you calculate y for various values of alpha, you can see that the summation is always very small.

Yes, but these are roundoff errors. As Richard had shown the sum should always total to a perfect zero as in every of the two sets of three sines they are phase shifted by exactly 1/3 od their period!

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