I get something similar, so you might want to check:
v2 = (1/M)*(-k*x2 + 2*(m1*g - Ff)*x
where: M = m1 + m2
Which, when values are plugged in, boils down to
v2 = -33.33(N/kg/m)*x2 + 0.1380(N/kg)*x
I think it must be an equivalent form.
I got that it was the square root of 1/3. I've had this confirmed by 2 people now.
Edit: Nope, you're right. Using exact values, it still works out to be the square root of 1/3.
Well... I tried it using the form you got. I got slightly more than the square root of 1/3. However, I just saw the same question done using de Moivre's theorem, and the answer was the square root 1/3.