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A confusing question

  1. May 4, 2007 #1
    A body of mass m moves under the influence of a force F in two dimensions. It has an trajectory
    r(t) = aCos(wt)x^ + bSin(wt)y^

    a = alpha
    b = beta
    w = omega, they are not a, b, and w in alphabet
    x^,y^: vector unit

    a,b,w are constant. Find the force law F = F(r) which corresponds to this motion (This trajectory is an ellipse, but not Keplerian ellipse. Newton's Law of Gravitaion is not the force law you seek here).
     
  2. jcsd
  3. May 4, 2007 #2
    Hint: Newton's second law of motion.
     
  4. May 4, 2007 #3
    Can you explain more in detail, it still confuses me. How do we derive the fomular of Newton's Second Law F=ma to this kind of fomular:confused:
     
  5. May 4, 2007 #4

    Hootenanny

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    Well we have;

    [tex]\vec{F} = m\vec{a}[/tex]
    [tex]\vec{F} = m\frac{d\vec{v}}{dt}[/tex]
    [tex]\vec{F} = m\frac{d^2\vec{r}}{dt^2}[/tex]

    Can you go from here?
     
    Last edited: May 4, 2007
  6. May 4, 2007 #5
    I have to admit that I'm stupid, I know the Newton's Second Law. But how to get to r(t) = aCos(wt)x^ + bSin(wt)y^
     
  7. May 4, 2007 #6
    What does [tex]m\frac{d^2\vec{r}}{dt^2}[/tex] mean to you?
     
  8. May 4, 2007 #7

    Hootenanny

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    My god man! I've forgot my d's! Duly corrected ...
     
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