Two simple harmonic motions of angular frequency `100 rad s^(-1)` and `1000 rad s^(-1)` have the same displacement amplitude. The ratio of their maximum accelerations is

Options

A. `1:10^(3)`
B. `1:10^(4)`
C. `1:10`
D. `1:10^(2)`

Answer

D

Explanation

Given that, `omega_(1)=100 `rad/s
`omega_(2)=1000`rad/s
`a_("max"_(1))=omega_(1)^(2)A`
`a_("max"_(2))=omega_(2)^(2)A`
`therefore (a_("max"_(1)))/(a_("max"_(2)))=(omega_(1)^(2))/(omega_(2)^(2))=((100)^(2))/((1000)^(2))=(1)/(10^(2))`