Is Mechanical Energy Conserved During Swinging at a Lake Hangout?"

[geauxKTM]

Homework Statement

at a lake hangout there is a tree to swing from over the lake.. Friend is scared and doesn't let go and swings back and forth severall times without stopping. Is his mechanical energy conserved during the swinging process?

Homework Equations

The Attempt at a Solution

 

[geauxKTM]

I know its potential and kinetic energy

 

[J--me]

If he doesn't 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.

 

[J--me]

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