Fraction of total energy which is kinetic `=(K.E.)/(T.E.)`
`=((1)/(2)momega^(2)(a^(2)-y^(2)))/((1)/(2)m omega^(2)a^(2))=(a^(2)-y^(2))/(a^(2))=(a^(2)-(a^(2))/(4))/(a^(2))=(3)/(4)`
Fraction of total energy which is potential
`=(P.E.)/(T.E.)=((1)/(2)momega^(2)y^(2))/((1)/(2)momega^(2)a^(2))=(y^(2))/(a^(2))=(a^(2)//4)/(a^(2))=(1)/(4)`
KE `=` PE
`(1)/(2)momega^(2)(a^(2)-y^(2))=(1)/(2)momega^(2)y^(2)`
On solving , `y=a//sqrt(2)`