The time period of a particle in simple harmonic motion is 8 second. At t = 0 it is at the mean position. The ratio of the distances travelled by it in the first and second is :

Options

A. `1//2`
B. `1//(sqrt(2)-1)`
C. `1//sqrt(2)`
D. `1//sqrt(3)`.

Answer

B

Explanation

`y=r sin omega t`
`:. Y_(1)=r sin omega xx 1` and `y_(2)=r sin omega xx2`.
`:." "(y_(1))/(y_(2))=(sin omega)/(sin 2omega)=(1)/(2 cos omega)=(1)/(2.cos""(2pi)/(T))=(1)/(2 cos((2pi)/(8)))`
`:." "(y_(1))/(y_(2))=(1)/(sqrt(2)):.y_(2)=sqrt(2)y_(1)`
`:.` Distance covered in `2"nd"=y_(2)-y_(1)=sqrt(2)y_(1)-y_(1)`
`=(sqrt(2)-1)y_(1)`
`:.` ratio of distances covered in Ist second and 2nd second `=(1)/(sqrt(2)-1)`
Correct choice is (b).