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Potential energy curve

  1. Sep 29, 2011 #1
    1. The problem statement, all variables and given/known data
    Prove the expressions for c and w

    c=re

    w=(k/m)^1/2


    2. Relevant equations

    V(r) =k/2*(r-re)^2

    F=ma=m*d^2r/dt^2

    r=A*cos(wt)+B*sin(wt)+c

    3. The attempt at a solution

    dV(r)/dr =-k(r-re)

    m*d^2r/dt^2=-k(r-re)

    d^2r/dt^2=-k/m*r+k/m*re

    r=A*cos(wt)+B*sin(wt)+c

    d^2r/dt^2= -A*w^2*cos(wt)-B*w^2*sin(wt)

    -A*w^2*cos(wt)-B*w^2*sin(wt)=-k/m*(A*cos(wt)+B*sin(wt)+c)+k/m*re

    I am stuck at this point I do not see how to eliminate each side. Any help would be appreciated.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 29, 2011 #2

    vela

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    Could you please tell us the problem statement as it was originally given?

    You might want to consider the change of variables r' = r-re.
     
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