# Differential equation (probably)

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Itsmikeysfault

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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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RDKGames

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#2

(Original post by

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.

**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.

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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Itsmikeysfault

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#3

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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

**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

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Itsmikeysfault

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#4

**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

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mqb2766

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Are you sure you have to solve the problem by setting up/solving an ODE?

What have you covered on dimensional analysis?

What have you covered on dimensional analysis?

Last edited by mqb2766; 1 month ago

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(Original post by

Are you sure you have to solve the problem by setting up/solving an ODE?

What have you covered on dimensional analysis?

**mqb2766**)Are you sure you have to solve the problem by setting up/solving an ODE?

What have you covered on dimensional analysis?

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mqb2766

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(Original post by

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

**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

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

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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

**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

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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mqb2766

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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?

**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?

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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