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umep physics thread

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Mao:
No. the characteristic equation to is , which has complex solutions

When you have p as a complex number , the general solution is

Hence in this case, , since , the exponential term equals to 1.


Proof of general solution where p are complex conjugates :



By Euler's formula

/0:
oh yeah, thanks mao...

I got the sign wrong >_<

Thanks for the proof too mao :D

/0:
Is it true that the point joining two ropes of different linear mass density is a node in a standing wave? Is there a way to prove this?


Also, for joined ropes, if you send a pulse down the first rope, then and , where is the velocity in the first rope and in the second.

If you let (i.e. the second rope doesn't exist) then , but that means that and !

How can it be +2?

/0:
Just learnt about Gauss Law, and it seems to simplify lots of problems...

If you use coulomb's law you can find the field from a non-infinite plate or non-infinite rod but is this possible with Gauss' Law?


Also, just wondering, is there a flux type thing for gravity?

Like, say the gravitational flux was D, then by analogy would this expression for the flux through a sphere hold?

i.e.

mark_alec:
Yes

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