How Does the Conservation of Energy Principle Apply to a Gymnast's Swing?

[tutojean]

Homework Statement

Example: A 50 kg gymnast does giant circles around a horizontal bar. At the top of her swing her center of mass is 1.0 m above the bar traveling 1.2 m/s. what is the speed of her center of mass at the bottom of her swing where her center at mass is 1.0 m below the bar? ( No given diagram)

Homework Equations

[K + Eg + Es] = [K + Eg + Es + Ef]
Initial Final

K=1/2mv^2
Eg=mgh
Es= 1/2 kx^2
Ef= uND

The Attempt at a Solution

What I did: [K] = [K + Eg]
or either [ Eg] = [K}. Please help me with setting this problem up. The first set up didn't work for me and I'm just needing help setting the problem up. No need for figuring out the problem. Thank You

 

[rock.freak667]

If we take the bar she is swinging from as having 0 potential and kinetic energy, that the top of her swing, what types of energy does he have and what the total energy she has due to these two types?