Math..............

poppins9000

Any1 got any decent maths notes or knoe where to get any.....
And any1 want to enlighten me on this q -
Differentiation- if x = a.coswt + b.sin.w.t, where a,w,t,b are constants..
show that
d2x + w2x = 0
dt2

2's supposed to be squared btw..............???????????

and trig........ just not my cup of tea..........

seamus

Well, where you need to start, is look at what you have, and what you need.

you have an x, and you need a d^2x. You first clue is: differentiate.

poppins9000

ok obviously nuf i gathered that 1!!................ :eek:
it just dont seem to work out right............
can you do it so...............?

*Angel*

poppins9000 wrote:

Differentiation- if x = a.coswt + b.sin.w.t, where a,w,t,b are constants..
show that
d2x + w2x = 0
dt2

surely if it's d2x/dt2 then the 't' cannot be a constant? Check that you wrote it down right...

*Angel*

Okay so here you go,

x = acos(wt) + bsin(wt)

dx/dt = -awsin(wt) + bwcos(wt)

d2x/dt2 = -aw2cos(wt) - bw2cos(wt)

d2x/dt2 = -w2(acoswt + bsinwt) = -w2x

dudara

*angel* is right. What you're actually doing here is showing that the expression y = aSin(wt) + bCos(wt) satisifies the differential eq you were given.

First off, rewrite it

d2y/dt2 = -w^2y

so you're being asked to show that the 2nd derivative of the expression you were given equals the original expression times w^2

y = aSin(wt) + bCos(wt)

dy/dt = waCos(wt) - bwSin(wt)

d2y/dt2 = -w^2aSin(wt) -w^2bCos(wt)
= -w^2(aSin(wt) + bCos(wt))
= -w^2(y)

poppins9000

Yeah.......i did right it down wrong,just rang my mate.....that would've been smart of me!
reckon i was just making a stupid mistake..... leaving out the minus sign when dif it..........AH how annoying..
Anyhoo cheers guys.............

tinkerbell

If you want a decent maths book, don't bother with those revision books.

Get Text & Tests 4 & 5 - they are fantastic. I worked through those two books for my Leaving revision (we used a different book at school) and they are so much better than any other maths book I used while in school. Then again, that was four years ago - unless the course has changed since then?

D-Generate

As the applied maths students should be able to see, thats S.H.M and the amplitude is sqrt(a^2 + b^2)

chickens

Here are good sites: http://www.netsoc.tcd.ie/~jgilbert/maths_site/index.html
http://mthwww.uwc.edu/wwwmahes/courses/math/mm110exs.htm#absineq
http://www.math.armstrong.edu/MathTutorial/
http://members.lycos.co.uk/Physics/lc1.htm

Godd luck.

Rredwell

tinkerbell wrote:

Get Text & Tests 4 & 5 - they are fantastic. I worked through those two books for my Leaving revision (we used a different book at school) and they are so much better than any other maths book I used while in school. Then again, that was four years ago - unless the course has changed since then?

Well, there are new TT4 and TT5 now - the chapters are swapped around a bit - and they are great, I agree.

What book did you have, Tinkerbell? Discovering Maths?

D-Generate

Must say I like Discovering Maths, questions are tougher than the actual papers so its good practice.

dudara

I'm giving LC Honours Maths grinds at the moment to a guy using TT4 and TT5. To be honest, I prefer discovering Maths. I think it's a higher standard of book.

*Angel*

I personally like the Text and Tests 4 & 5 (new versions) but I haven't used any others so... I don't like revision books for maths though.

poisonapplet is an ok site for the leaving cert.

*EDIT* Is anyone here doing the further geometry option question in paper I, cos I can't find stuff for it anywhere, not even in books?