Total Energy of an Simple Harmonic Motion is given as

1/2m(wA)^2

Kinetic energy for any Simple Harmonic Motion can be written as

1/2 m(wA)^2 cos^2(wt).

so for 75% KE,

3/4 * 1/2 m(wA)^2=1/2 m(wA)^2 cos^2(wt)

=> ((3)^1/2)/2=cos(wt)

we get , wt = pi / 6

w=2 pi/T

t=T/12 = 1/6 seconds.

So the answer is 1/6 seconds