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Sarahisme

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Everything posted by Sarahisme

  1. so i still think its right.....but i guess it isnt hey?
  2. Hi all, i am just having a little bit of a problem with part © of this question.... i get [math] \frac{dr}{dt} = r^3 [/math] and so [math] r(t) = -\frac{1}{\sqrt{2t}} [/math] this doesnt seem right to me....but what do i know! also i can't see how to get [math] \frac{d \theta}{dt} [/math] any ideas guys? Thanks Sarah
  3. hmm ok let me have a go at that... for the 'moving together' type of normal mode oscillation (mode 1):: frequency = [math] \frac{p}{2 \pi} = \frac{\sqrt{k}}{2\pi} [/math] for the 'moving oppositely' type of normal mode oscillation (mode 2):: frequency = [math] \frac{q}{2 \pi} = \frac{\sqrt{k+2nk}}{2\pi} [/math] so we can see that mode 1 is [math] \sqrt{1+2n} [/math] times faster than mode 2. however i'm not sure about "relative phase of the oscillations."....??
  4. ok i'll explain how i got it.... i used exact equations method. i.e. [math] M_y = N_x [/math] rearranging the equation to : [math] (x^2-y^2-1) + (2xy)y' = 0 [/math] but the equation is not exact to start with so have to find integrating factor. i found this integrating factor to be [math] \frac{1}{x^2} [/math] multiplying this through the original equation gives [math] (1-\frac{y^2}{x^2}-\frac{1}{x^2}) + (\frac{2y}{x})y' = 0 [/math] the equation is now exact. and so solving it gives the answer i found: [math] x + \frac{y^2+1}{x} = c [/math]
  5. when they say sketch solution curves do you think they mean draw a phase portrait or something else?
  6. hmm well actually i got the equation [math] x + \frac{y^2+1}{x} = c [/math] which produces a contour plot like this but that doesnt seem to relate to the critical points found hmmm..... me confuseled
  7. dont worry think i got it, exact equations right? yay!
  8. ok here goes, what do you think...: i get the two eigen vectors to be [1,1] and [1,-1] (pretend that those brackets are vertical. so i get the solution to be: [math] x_1 = rsin(pt + \theta) + s sin(qt + \phi) [/math] [math] x_2 = rsin(pt + \theta) - s sin(qt + \phi) [/math] where [math] p = \sqrt{k} [/math] and [math] q = \sqrt{k+2nk} [/math] and then choosing r = 1, s = 0 gives the 'moving together' type of normal mode oscillation and r = 0 , s = 1 gives the 'moving oppositely' type of normal mode oscillation. is that the right sort of thing? l mean, does it answer the "under what conditions can this system be made to oscillate in a preciisely periodic manner?" bit of the question??
  9. hmm the question seems to have disappeared, so here it is again :
  10. there are two normal modes: (1) where the two masses are moving in the same way (in the same periodic motion) (2) where the two masses are always moving in opposite directions (in a periodic way) i think thats right? i am guessing that i need to solve this problem using a system of first order linear equations.....?
  11. hmm got (a) its part (d) that i can't seem to get now.... how can you integrate this: [math] \frac{dy}{dx} = \frac{1-x^2+y^2}{2xy} [/math] i am assuming thats how you find the 'complete solution' right?
  12. are you just talking about how to do the "show that the equations governing the motion are..."? i can get this bit , writing down those equations, its the other stuff where everything goes horribly wrong
  13. hey, sorry for all the questions lately but .... for this is question, is the only critical point (1,0) ? it keeps refering to critical pointS in the problem... but i think there is the only the one critical point, right? as for the rest of the question, well i suppose i need to figure this little kenumdrem (spelling? ) out first, hey thanks, and apologies for the questions again! -Sarah
  14. hey all damn this problem, i have spent hours at it and keep ending up in a big mess... any ideas guys? :S Sarah
  15. oh ok i get it now! thanks swantsont -Sarah
  16. you've lost me i think... to get my above answer i set [math] w = \frac{w_1+w_2}{2} [/math] and [math] k = \frac{k_1+k_2}{2} [/math] and its a plane wave?
  17. i think they are: [math] v_{phase} = \frac{w}{k} [/math] and [math] v_{group} = \frac{dw}{dk} [/math]
  18. hmmm ok so i get: [math] 2A e^{i(kx-wt)} cos( \frac{k_1 x-k_2 x-w_1 t+w_2 t}{2}) [/math] i think thats ok.... but as for the phase and group velocities...???
  19. why set [math] k_1{x}-w_1{t}=\pi=k_2{x}-w_2{t} [/math] ? why is it to pi? i'm not quite following...
  20. hey everyone hmm...can't seem to work out how to attack this question.... any suggestions guys? Cheers Sarah
  21. Hi all, i have done this question which involves capillary waves. where we started with [math] \lambda \propto \lambda^{-3/2} [/math] then i found that [math] v_{phase} = \frac{\lambda^{-1/2}}{2\pi} [/math] and [math] v_{group} = \frac{3\lambda^{-1/2}}{4\pi} [/math] and thus taking the ratio of the two gives that the group velocity is 1.5 times the the phase velocity. I am them asked to explain the meaning of this result, and i am a little unsure of how to answer that.... any ideas/hints etc.? Cheers Sarah
  22. k thanks, i got it now! thanks for all your help btw!
  23. how do i work out the Z number for U-235 and Pu-239?
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