HSC 2012 MX1 Marathon #2 (archive) (1 Viewer)

[Sy123]

Re: HSC 2012 Marathon

Prove that the acceleration of a body a is given by a=v(dv/dx) where x and v are the displacement and velocity of the particle after a time t.

Ill edit one in as soon as I can think of one (a question)

 

[Sy123]

Re: HSC 2012 Marathon

Ok, Ive got a good premise for a question. But I dont know enough to make the question more creative. But yeah here we go.

 

[bleakarcher]

Re: HSC 2012 Marathon

Ok, Ive got a good premise for a question. But I dont know enough to make the question more creative. But yeah here we go.

centre of oscillation is directly proportional to time, so centre of oscillation is changing?

 

[Sy123]

Re: HSC 2012 Marathon

Yes very much so.

 

[bleakarcher]

Re: HSC 2012 Marathon

I'd answer this question but I am very confused as to the motion of the particle. I mean the particle moves "in a sort of SHM", really?

 

[Sy123]

Re: HSC 2012 Marathon

There are 4 hints to tell you to use a trigonometric function.
"Amplitude"
"Period"
"Inverse Trig value for v=0"
"a sort of S.H.M."

Im sorry if its not too clear though. Like I said, I thought of the premise on the top of my head, and it took me a while to figure out what to ask

 

[barbernator]

Re: HSC 2012 Marathon

it should be a form of SMH about the line y=x right? kinda like the GDP curve?

 

[bleakarcher]

Re: HSC 2012 Marathon

you cant have SHM though without a defined centre of oscillation if the amplitude is constant. it just doesnt make sense to me.

 

[Sy123]

Re: HSC 2012 Marathon

Your in the right track barbenator

BIG SPOILER HINT:

in a sin (nt+alpha)+b, b = kt

 

[barbernator]

Re: HSC 2012 Marathon

i rly cbfd to do the question atm, but one way you could do it is to use cis(45) to rotate the sin curve.(i know its better to just do sy123's spoiler, but rotation would be a cool way )

 

[bleakarcher]

Re: HSC 2012 Marathon

Your in the right track barbenator

BIG SPOILER HINT:

in a sin (nt+alpha)+b, b = kt

I had that in mind originally but how would the particle actually be moving? This isn't a maths question, i know.

 

[barbernator]

Re: HSC 2012 Marathon

I had that in mind originally but how would the particle actually be moving? This isn't a maths question, i know.

--------->
<------
--------->
<------
--------->
<-------
--------->
where left to right is displacement

whoops, the arrows all go to the side. NVM ill say it in words. the particle would displace to the right, and then reach a maximum and move back to the left, except it would not move as far back, and then move to the right again but further this time, and then back again but not as far, etc etc

 

[bleakarcher]

Re: HSC 2012 Marathon

--------->
<------
--------->
<------
--------->
<-------
--------->
where left to right is displacement

whoops, the arrows all go to the side. NVM ill say it in words. the particle would displace to the right, and then reach a maximum and move back to the left, except it would not move as far back, and then move to the right again but further this time, and then back again but not as far, etc etc

wouldnt it move just as far back because amplitude is constant?

 

[bleakarcher]

Re: HSC 2012 Marathon

oh wait, no, I get it

 

[bleakarcher]

Re: HSC 2012 Marathon

thanks barbenator

 

[RealiseNothing]

Re: HSC 2012 Marathon



lol I'll try make up a proper 3U question.

 

[bleakarcher]

Re: HSC 2012 Marathon

pi

 

[bleakarcher]

Re: HSC 2012 Marathon

That involves the Basel Problem though, I ain't proving that shit lol.

 

[bleakarcher]

Re: HSC 2012 Marathon

It's done in q8 of the 2010 mx2 hsc paper though, I was looking at it earlier today.

 

[RealiseNothing]

Re: HSC 2012 Marathon

That involves the Basel Problem though, I ain't proving that shit lol.

It's not that hard of a proof tbh.