A simple harmonic oscillator has an amplitude a and time period T. The time required to travel from x=a to x=a/2 is

x=asin⁡ωt=asin⁡2πTt  Now a2=asin⁡2πTt  or  sin⁡2πTt=12 or  sim 2πTt=sin⁡π6  or  t=T/12  For x=a  we have t=T/4  So, the time taken to travel from x=a to x=a/2 =T/4−T/12=T/6