The period of a particle in SHM is 8 sec. At t = 0, it is at the mean position. The ratio  of the distances travelled by it in the first one second and in the 2nd one second is

At t = 0, let particle move in +x direction. So, equation of SHM is :  x=AsinωtNow,  ω=2πT=2π8=π4  So,  x=Asinπt4v=Aπ4cosπt4 Distance travelled in t seconds,  d=∫0tvdtWhen  0<πt4<π2   or   0