# Simplify this equation.

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#1
I'm going out of my mind here but I can't seem to simplify this equation.

What do you get when substituting into both sides?

EDIT: is a constant.

Would I be right in saying on the left side you would get ?
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6 years ago
#2
(Original post by Dr Alcoholic)
I'm going out of my mind here but I can't seem to simplify this equation.

What do you get when substituting into both sides?
Let me just check with Stephen Hawkins
1
#3
(Original post by Old_Simon)
Let me just check with Stephen Hawkins
Who?
0
6 years ago
#4
(Original post by Dr Alcoholic)
Who?
Hawking. typo don't stress.
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#5
(Original post by Old_Simon)
Hawking. typo don't stress.
Maybe you can ask him to give me a new brain while you're at it.
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6 years ago
#6
That question is a joke.
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#7
I don't mean to be rude, but this is stressing me out so could you only leave a comment if you know how to do this please.
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6 years ago
#8
Calculate the second partial derivatives of your given substitution. Substitute it in.
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6 years ago
#9
I had a go, didn't really get it, but here is what i came out with:

*I tried my very best, so don't be mad if i didn't help

All the best,
Reety.
1
#10
(Original post by Reety)
I had a go, didn't really get it, but here is what i came out with:

*I tried my very best, so don't be mad if i didn't help

All the best,
Reety.

TBH it's further than I've got.
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#11
(Original post by BlueSam3)
Calculate the second partial derivatives of your given substitution. Substitute it in.

Does that imply that , where is the phase speed?
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6 years ago
#12
What is this for? I'm sensing a mechanics module?
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#13
(Original post by RhymeAsylumForever)
What is this for? I'm sensing a mechanics module?
No it's to do with transmissions. I'm not a maths student, it's engineering but this is a maths based problem hence I'm asking for help from maths people.
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6 years ago
#14
(Original post by Dr Alcoholic)
No it's to do with transmissions. I'm not a maths student, it's engineering but this is a maths based problem hence I'm asking for help from maths people.
Oh ok, looked a bit like further maths with physics.
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6 years ago
#15
I had another crack at it, here is what i got:

Hope this helped
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6 years ago
#16
(Original post by Dr Alcoholic)
Does that imply that , where is the phase speed?
The image is broken, so I can't tell you, sorry.
0
6 years ago
#17
(Original post by Dr Alcoholic)
I'm going out of my mind here but I can't seem to simplify this equation.

What do you get when substituting into both sides?

EDIT: is a constant.

Would I be right in saying on the left side you would get ?
If this hasn't been sorted yet, yes the LHS there is correct.

The RHS is even easier - notice that the "" factor in is a constant w.r.t. . So when you differentiate w.r.t. z twice for the RHS, the can be pulled out of the derivative, leaving only the E(z) factor to be operated upon.

This should give you a second order linear differential equation for , which you should be able to solve.
1
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