The time period of a simple harmonic motion is 8 s At t=0. it is at the mean position.The ratio of the distance travelled bi it in the first and second seconds is,

Options

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

Answer

D

Explanation

Distance travelled in I second `y_(1) = A sin ((2pi)/(8) xx 1) = (A)/(sqrt(2))`
distance travelled in 2 seconds = A
distance travelled in 2nd second `y_(2) = A - (A)/(sqrt(2)),`
`(y_(1))/(y_(2)) = ((A)/(sqrt(2)))/(A - (A)/(sqrt(2))) = sqrt(2) + 1`