Potential energy curve

prize fight

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

vela

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

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