## Potential energy curve

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
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 Recognitions: Gold Member Homework Help Science Advisor Staff Emeritus 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.

 Tags curve, energy, harmonic, motion, potential