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- In what cases does dimensional analysis fails? And also is there like any preferred situation or an 'ideal' situation in order to use dimensional analysis? Thanks in advance!
It possible a diagram would be really really helpful
Well, a number of quantities are dimensionless, but I'm not sure that represents a failure. Can you think of some dimensionless constants or quantities that are used commonly?Summary: In what cases does dimensional analysis fails?
That's like asking when addition doesn't work - when it's the wrong tool for the job. Maybe you need to subtract or to multiply.I just thought well obviously this won't work for evert case so I just wanted to know what are those cases.
Thanks for the links!Well, a number of quantities are dimensionless, but I'm not sure that represents a failure. Can you think of some dimensionless constants or quantities that are used commonly?
Also, these two PF Insights articles would probably be good background reading for you to help understand dimensional analysis better...
Learn the Basics of Dimensional Analysis
This intent of this Insight is therefore to provide a basic introduction to the subject with a number of examples with which the reader may be familiar.www.physicsforums.com
Make Units Work for You
How do we use units? You may see one of these speed limit signs, nearly every day. Even though neither of them display units, drivers know they are implied.www.physicsforums.com
No no not like that. What if sometimes we don't know the nature of the opposing quantity. How are you going to proceed then?That's like asking when addition doesn't work - when it's the wrong tool for the job. Maybe you need to subtract or to multiply.
Dimensional analysis cannot tell you if the circumference of a circle is 6r, 2πr or 7r. It can tell you it is not 1/r or r^{2}.
I don't understand.What if sometimes we don't know the nature of the opposing quantity.
Like in damping of harmonic oscillations.I don't understand.
What do the overall dimensions of the quantity in the exponent need to be? So what does that tell you about the dimensions of λ ?Like in damping of harmonic oscillations.
For example damping in oscillations. What if we dont know the nature of damping? How do you find the equations of motion?I still don't understand. Perhaps you could use complete sentences? Maybe even paragraphs?
What does that have to do with dimensional analysis?How do you find the equations of motion?
Please see post #10.For example damping in oscillations. What if we dont know the nature of damping? How do you find the equations of motion?
I am asking using dimensional analysis how do you find the eqaution of motion thenWhat does that have to do with dimensional analysis?
Sorry I am new here. Post 10 where?Please see post #10.
That's actually really helpful. Thanks.No worries. The post number in each thread is shown in the upper right of each post. This post of mine will likely be #17, since I'm replying to your post #16. So just scroll up the thread to look for my reply in post #10. It was a post showing some equations from Hyperphysics to help you see the typical differential equation and solution for a damped harmonic oscillator.
So I cannot use dimensional analysis in such cases?That's actually really helpful. Thanks.
So I cannot use dimensional analysis in such cases?No worries. The post number in each thread is shown in the upper right of each post. This post of mine will likely be #17, since I'm replying to your post #16. So just scroll up the thread to look for my reply in post #10. It was a post showing some equations from Hyperphysics to help you see the typical differential equation and solution for a damped harmonic oscillator.
Like in the Hyperphysics equations? Sure. Can you show the dimensions for each of the terms in the initial differential equation? And then show how that helps to define the dimensions of λ in the end?So I cannot use dimensional analysis in such cases?
I think I can. I can show the complimentary function for x. Then I can By eliminating the constants by plugging in the initial conditions, we can find the dimensions of lambdaLike in the Hyperphysics equations? Sure. Can you show the dimensions for each of the terms in the initial differential equation? And then show how that helps to define the dimensions of λ in the end?
Okay, but what are the dimensions (or units) for each of the terms in these equations?I think I can. I can show the complimentary function for x. Then I can By eliminating the constants by plugging in the initial conditions, we can find the dimensions of lambda
The dimensions of c are...?I think I can. I can show the complimentary function for x. Then I can By eliminating the constants by plugging in the initial conditions, we can find the dimensions of lambda