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## Homework Statement

A harmonic oscillator with a vertical mass on a string has a hanging mass of 2m and a spring constant of K. It oscillates with an amplitude of Z. When its position is at a distance Z/2 of the equilibrium point, its potential energy is U

_{i}. What is the maximum kinetic energy K

_{m}?

## Homework Equations

E=1/2mV

^{2}+ 1/2mA

^{2}

## The Attempt at a Solution

I realized that the max kinetic energy must be equal to the to the max potential energy because total energy is constant. I just don't know where to put the equations to make it fit.

Can someone show me the set up? The answer give was K

_{m}= 4U

_{i}

Thanks in advance!