Two simple harmonic motions are represented by the equations `y_(1) = 10 sin (3pit + (pi)/(4))`
and `y_(2) = 5 (3 sin 3 pi t+sqrt(3) cos 3 pi t)`. Their amplitudes are in the ratio of

Options

A. `sqrt(3)`
B. `1//sqrt(3)`
C. 2
D. `1//6`

Answer

B

Explanation

Given that `y_(1) 10 sin (3pit + (pi)/(4))`
and `y_(2) = 5(3sin 3pit + sqrt(3) cos 3pit)`
or `y_(2) = 10sqrt(3) sin (3pit + 30^(@))`
`therefore` Ratio of their amplitudes
` = (10)/(10sqrt(3)) = (1)/(sqrt(3))`