If two SHMs are represented by equations `y_(1) = 5 sin (2pi t + pi//6) and y_(2) = 5 [sin (3pi) + sqrt3 cos (3pi t)]`. Find the ratio of their amplitudes.

Explanation

As `y_(2) = 5 sin (3pi t) + 5 sqrt3 cos (3pi t)`
Let, if `5 = A cos phi and 5 sqrt3 A sin phi`
`rArr " so " A = sqrt(5^(2) + (5 + sqrt3)^(2)) = 10 and tan phi = (5 sqrt3//5) = sqrt3 rArr phi = pi//3`
`y_(2) = A cos phi sin 3pi t + A sin phi cos 3 pi t rArr y_(2) = 10 sin {(3pi t + (pi//3)}`
So `A_(1)//A_(2) = 5//10 = 1//2`