Only Elastic Force x_1

`v_1 = sqrt(( m * v_2 ^2)/ k + x_2 ^2-( m * v_1 ^2)/ k )`

`(v_1)"Initial Velocity"`

`(v_2)"Final Velocity"`

`(k)"Spring Constant"`

`(m)"Mass"`

`(x_2)"Final Position"`

University Physics 12th Edition, Chapter 7, Equation #7.12