MHB Problems with propagation of error

[bobey]

I have problem regarding the propagation of error since the equations involving mixtures of multiplication, division, addition, subtraction, and powers. Please help me to clarify whether my attempts are right or wrong.

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[Sudharaka]

I have problem regarding the propagation of error since the equations involving mixtures of multiplication, division, addition, subtraction, and powers. Please help me to clarify whether my attempts are right or wrong.

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Hi bobey, :)

I think you should review how to calculate the propagation of errors. One of the basic things that you should remember is to neglect the constant values of the formulas when deriving the error propagation formula. For example take your Question 1.

\[D=-\frac{L}{4m}\]

Now, the error propagation formula would be,

\[\frac{\Delta D}{D}=\sqrt{\left(\frac{\Delta L}{L}\right)^2+\left(\frac{\Delta m}{m}\right)^2}\]

Even if you have the formula, \(\displaystyle D=\frac{L}{m}\) you get the same error propagation formula above. The constant \(-\frac{1}{4}\) have no significance.

Read http://www.fas.harvard.edu/~scphys/nsta/error_propagation.pdf and this to find out how to derive the error propagation for any given formula.

Kind Regards,
Sudharaka.

 

[CaptainBlack]

Hi bobey, :)

I think you should review how to calculate the propagation of errors. One of the basic things that you should remember is to neglect the constant values of the formulas when deriving the error propagation formula. For example take your Question 1.

\[D=-\frac{L}{4m}\]

Now, the error propagation formula would be,

\[\frac{\Delta D}{D}=\sqrt{\frac{\Delta L}{L}+\frac{\Delta m}{m}}\]

I would check this if I were you.

CB

 

[bobey]

Problems with propagation of error for multiple variables

please help by telling me whether my approach to solve the problems are right or wrong. please refer to the ATTACHMENT for the questions and my approaches...

your help is highly appreciated!

question 1
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question 2
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[CaptainBlack]

Re: Problems with propagation of error for multiple variables

please help by telling me whether my approach to solve the problems are right or wrong. please refer to the ATTACHMENT for the questions and my approaches...

your help is highly appreciated!

question 1
View attachment 336

For this one you should not need the square and square root, they cancel, and anyway you only use a root sum of squares composition of errors when there is more than one variable involved.

CB

 

[CaptainBlack]

Re: Problems with propagation of error for multiple variables

please help by telling me whether my approach to solve the problems are right or wrong. please refer to the ATTACHMENT for the questions and my approaches...

your help is highly appreciated!

question 1
View attachment 336
question 2
View attachment 337

For the second the same comment as for the first, otherwise OK (except you should transfer the minus sign attached to the 2 to the whole expression.

CB