Energy conservation problem?

Potential energy in a spring: Esp = (kx^2)/2

Kinetic energy: Ek = (mv^2)/2

The total energy of the system Etot = Esp + Ek is kept constant because of the

conservation of energy.

When the block is pulled to x=49cm it has the maximum potential energy and zero

kinetic energy:

E = Esp(max) + 0

When it is released potential energy starts to convert into kinetic enrgy. At postion

x=0 kinetic energy reaches its maximum so:

E = 0 + Ek(max)

Again at x=-49cm potential energy will reach max. and so on back and forth.

Somewhere along the way Ek=Esp will occur

Esp(max) = (kx^2)/2 = (16×0.49^2)/2 = 1.92 J = Etot

If Esp = 1.92/2 = 0.96 J = Etot/2 it means Ek = 0.96 J

Esp = (kx^2)/2 = 0.96 J => x = ±√((2×0.96)/k) = ±0.346

----> Esp will equal Ek at positions 34.6cm and -34.6 cm

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