and ${y_2} = 5[\sin 3\pi t + \sqrt 3 \cos \,3\pi t]$ 

$ = 5 \times 2\,\left[ {\frac{1}{2} \times \sin 3\pi t + \frac{{\sqrt 3 }}{2} \times \cos 3\pi t} \right]$

$ = 10\,\left[ {\cos \frac{\pi }{3}\sin 3\pi t + \sin \frac{\pi }{3}\cos \pi t} \right]$

$ = 10\,\left[ {\sin \,\left( {3\pi t + \frac{\pi }{t}} \right)} \right]$ ...$ (ii)$     ( $\because$  $sin(A + B) = sinA \,cosB + cosA sinB)$ 

Comparing equation $ (i)$ and $(ii)$ we get ratio of amplitude $1 : 1.$