Mechanical energy, help quick

1. The problem statement, all variables and given/known dataat a lake hangout there is a tree to swing from over the lake.. Friend is scared and doesnt let go and swings back and forth severall times without stopping. Is his mechanical energy conserved during the swinging process?



2. Relevant equations



3. The attempt at a solution
 
I know its potential and kinetic energy
 
If he doesnt stop swinging back and forth then his mechanical energy is conserved but if he stops then his swing is being dampened, but in this case i would say that his mechanical energy is conserved.
 
E(mech) = E(pot) + E(kin)

E(kin) = 1/2mv^2 = 1/2m(A^2-x^2)w^2 = 1/2k(A^2-x^2)

E(tot) = 1/2kx^2 + 1/2k(A^2-x^2)

therefore the equation simplifies to give you one formula
 

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