# Differential equation (probably)

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#1
Can someone spot where I went wrong. I'm fairly sure the equation I get is correct as it correct as it satisfies the differential equation I set up. However, the question suggest you can isolate T which is not the case in my equation. Then, I tried working backwards and found that the function tau(lambda) must be a square root to so that the unit of the output is seconds. I then wrote e^x in its maclaurin form and noticed that if you discard terms greater than t^3, some stuff cancel and you get Tau(lambda) being a square root. However, I'm fairly sure this is a coincidence.

Last edited by Itsmikeysfault; 1 month ago
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1 month ago
#2
(Original post by Itsmikeysfault)
Can someone spot where I went wrong. I'm fairly sure the equation I get is correct as it correct as it satisfies the differential equation I set up. However, the question suggest you can isolate T which is not the case in my equation. Then, I tried working backwards and found that the function tau(lambda) must be a square root to so that the unit of the output is seconds. I then wrote e^x in its maclaurin form and noticed that if you discard terms greater than t^3, some stuff cancel and you get Tau(lambda) being a square root. However, I'm fairly sure this is a coincidence.

This is confusing … the question says h is a constant height from which the particle is released and yet you use h as the displacement variable… why?

Let x(t) be the displacement variable then form the ODE and solve it under the condition x(0)=h and x’(0)=0
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#3
(Original post by RDKGames)
This is confusing … the question says h is a constant height from which the particle is released and yet you use h as the displacement variable… why?

Let x(t) be the displacement variable then form the ODE and solve it under the condition x(0)=h and x’(0)=0
I originally used x but my teacher said to use h🤷*♂️
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#4
(Original post by RDKGames)
This is confusing … the question says h is a constant height from which the particle is released and yet you use h as the displacement variable… why?

Let x(t) be the displacement variable then form the ODE and solve it under the condition x(0)=h and x’(0)=0
If I solve using those initial conditions, I still can't isolate t?
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1 month ago
#5
Are you sure you have to solve the problem by setting up/solving an ODE?
What have you covered on dimensional analysis?
Last edited by mqb2766; 1 month ago
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#6
(Original post by mqb2766)
Are you sure you have to solve the problem by setting up/solving an ODE?
What have you covered on dimensional analysis?
I haven't covered anything about it. I watched a YouTube video earlier and apparently you can use it find out the units of something based on the other units in an equation. But I don't see how that would be that useful besides what I did on the left of the page
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1 month ago
#7
(Original post by Itsmikeysfault)
I haven't covered anything about it. I watched a YouTube video earlier and apparently you can use it find out the units of something based on the other units in an equation. But I don't see how that would be that useful besides what I did on the left of the page
So where is the question from/what is your level?

Ive not checked it carefully, but your solution is about right, though you'd normally not have zero initial conditions (initial height is zero?) as rdkgames noted. Not really a big problem though. The Maclaurin stuff isn't correct for the problem

Though the question is asking about dimensional analysis and this generally means not solving the ODE, rather considering the units in the ODE/differential equation. From a quick google, a couple of useful refs
http://people.whitman.edu/~hundledr/...3/dimanal2.pdf
https://citeseerx.ist.psu.edu/viewdo...=rep1&type=pdf

Looks like the problem is a slighlty mofified
https://www.damtp.cam.ac.uk/user/reh...-problems1.pdf
Last edited by mqb2766; 1 month ago
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#8
(Original post by mqb2766)
So where is the question from/what is your level?

Ive not checked it carefully, but your solution is about right, though you'd normally not have zero initial conditions (initial height is zero?) as rdkgames noted. Not really a big problem though. The Maclaurin stuff isn't correct for the problem

Though the question is asking about dimensional analysis and this generally means not solving the ODE, rather considering the units in the ODE/differential equation. From a quick google, a couple of useful refs
http://people.whitman.edu/~hundledr/...3/dimanal2.pdf
https://citeseerx.ist.psu.edu/viewdo...=rep1&type=pdf

Looks like the problem is a slighlty mofified
https://www.damtp.cam.ac.uk/user/reh...-problems1.pdf
It's an at interview assessment question for engineering at Cambridge. Thanks. I should be able to solve it with these.
This may be a stupid question but how did you find the question (well, a similar question) so easily? What did you google?
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1 month ago
#9
(Original post by Itsmikeysfault)
It's an at interview assessment question for engineering at Cambridge. Thanks. I should be able to solve it with these.
This may be a stupid question but how did you find the question (well, a similar question) so easily? What did you google?
I googled the topic to find the techniques and the question to find the question.
It ain't rocket science.

If its an interview assessment question, Im surprised that they're publically available beforehand. Is it legit - where did you get it from?
Last edited by mqb2766; 1 month ago
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