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remslie14-Alexandrite
14-Alexandrite
October 20, 2020
Solved

Velocity function will not integrate

Hi,

I am trying to simulate a base excitation using a velocity versus time waveform as the base excitation. I have imported an excel file and developed a velocity time function using "linterp". When I try to integrate this it flags an error.

Further down the sheet I use an indefinite integral to derive the base input displacement from my velocity waveform. Is this OK. Any assistance would be appreciated. Cheers Ross

AlanStevensAnswer
19-Tanzanite
October 20, 2020

1. In M15 the indefinite integral of sin(x) works ok!

g0.jpg

 

2.  I've fixed some errors in the sheet and pointed out some mistakes in units - see attached.

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6 replies

LucMeekes23-Emerald IV
23-Emerald IV
October 20, 2020

Your GY(t) is defined for only numerical applications. Asking for the indefinite integral (the integral without borders) is a symbolic operation. You can't even numerically evaluate an indefinite integral for symbolically known functions like sin(x):

LucMeekes_0-1603175719966.png

in contrast to:

LucMeekes_1-1603175748962.png

To determine the integral of the dataset that you input, simply summing is the best way.

Your datapoints are discrete values. You cannot achieve more accuracy by interpolation.

So:

LucMeekes_2-1603176536625.png

Success!

Luc

 

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remslie14-AlexandriteAuthor
14-Alexandrite
October 21, 2020

Luc,

Many thanks for your interest, knowledge  and feedback on my integration issue.

Cheers

Ross

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AlanStevens19-TanzaniteAnswer
19-Tanzanite
October 20, 2020

1. In M15 the indefinite integral of sin(x) works ok!

g0.jpg

 

2.  I've fixed some errors in the sheet and pointed out some mistakes in units - see attached.

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LucMeekes23-Emerald IV
23-Emerald IV
October 20, 2020

"In M15 the indefinite integral of sin(x) works ok!"

Yes, symbolically, but try that numerically...

 

Luc

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AlanStevens19-Tanzanite
19-Tanzanite
October 20, 2020

@ Luc

"Yes, symbolically, but try that numerically..."

 

Of course not numerically!  As you demonstrated, the result is a function, not a number (though I missed the fact that you'd shown a numerical = rather than a symbolic -> !).

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