Simple Harmonic Motion --> Trouble understanding velocity expressions -- help needed! (1 Viewer)

[blackops23]

Hi guy's just something I'm curious about involving velocity, specifically in the situation where there is simple harmonic motion.

So we know the expression that v^2 = (n^2)(a^2 - x^2) --> where a refers to amplitude (maximum displacement).

And thus v = +/- (n)[(a^2 - x^2)^0.5] ------- (1)

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However.... we know that x = a(cos(nt + alpha))

Therefore: dx/dt = -(n)(a)*[sin(nt + alpha)]

v= dx/dt
therefore v = -n(a)[sin(nt+alpha)] ------------------------ (2)

So we clearly have two expressions for v... are they both equal?
i.e. is -nasin(nt+alpha) = +/- n(a^2 - x^2)^0.5

and thus, is asin(nt+alpha) = +/-(a^2 - x^2)^0.5?

Or did I do something horribly wrong? Because I just can't see how they are equal...

Thanks, help is immensely appreciated.

 

[tambam]

Re: Simple Harmonic Motion --> Trouble understanding velocity expressions -- help nee

They are both expressions for velocity, but one is expressed in terms of x (displacement), and one is expressed in terms of t (time).

So yes, depending on what information you have, the velocity can be worked out in two ways to give the right answer.

 

[matrix1]

Re: Simple Harmonic Motion --> Trouble understanding velocity expressions -- help nee

lol it's so easy

also, tambam is an idiot. Has no idea wtf they are on about.

 

[thoth1]

Re: Simple Harmonic Motion --> Trouble understanding velocity expressions -- help nee

lol goodwin. i luv how u say the question is so easy but neva provide a solution. i also luv how u didnt even do 4U and u act like ur sum god of maffs. go fuk urself.

 

[roryclifford]

Re: Simple Harmonic Motion --> Trouble understanding velocity expressions -- help nee

course I know the answer, but why share it with u jerks?

I don't need to prove myself to you guys anymore. I did last year.

I have never been involved in an argument with you before, but as far as I can tell you spend oodles of your time making different accounts, posting under different names in different forums through the BOS website in order to simply insult others and act as a maths god.

As far as I can tell you DO feel the need to prove yourself to others, but in this case the proof is the measure of your douche-baggery.

Get off the forums, leave everyone on here alone and move on with your life.

 

[K4M1N3]

Re: Simple Harmonic Motion --> Trouble understanding velocity expressions -- help nee

I have never been involved in an argument with you before, but as far as I can tell you spend oodles of your time making different accounts, posting under different names in different forums through the BOS website in order to simply insult others and act as a maths god.

As far as I can tell you DO feel the need to prove yourself to others, but in this case the proof is the measure of your douche-baggery.

Get off the forums, leave everyone on here alone and move on with your life.

I think an OHSNAP! is in order.