Potential Energy Curve for Proving Expressions for c and w

[prize fight]

Homework Statement

Prove the expressions for c and w

c=re

w=(k/m)^1/2

Homework Equations

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

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

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

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.

 

[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.