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 :  displacement= x=Asinωt given T=8sec x=Asin2πTt x=Asin2π8t---(1)  displacement in t=1 first second is →from equatin (1)→ x1=Asin2π8(1)=A12 displacement in t=2 two seconds is →from equatin (1)→ x2=Asin2π8(2)=A ratio  of the distances travelled by it in the first one second and in the 2nd one second = x1 x2- x1 ratio=A2A-A2 ratio=12-1 rationalize ratio  of the distances travelled by it in the first one second and in the 2nd one second =2+1