Let K be the spring constant and Lbe the initial length in centimeter.
m(L+x1)w12=Kx1
and m(L+x2)w22=Kx2
Taking ratio
(L+x1L+x2)×(ω1ω2)2=x1x2
Now,
(ω1ω2)2=(12)2=14
x1=1
&
x2=5
Putting these value in above equation, we get,
(L+1L+5)×14=15⇒5L+5=4L+20 ⇒L=15 cm.