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

Explanation

`y_(2) = 5 (sin 4 pi t + sqrt(3) cos 4 pi t)`
`=5 xx 2 ((1)/(2) sin 4 pi t + (sqrt(3))/(2) cos 4 pi t)`
`= 10 ["cos"(pi)/(3) sin 4 pi t + "sin" (pi)/(3) cos 4 pi t]`
`rArr" "y_(2) = 10 sin (4pi t + (pi)/(3))`
Hence ratio of two amplitudes is `(A_(1))/(A_(2)) = (10)/(10) = 1 : 1`