The equations of two SHM are `y_(1)=10sin(4pit+pi/4),y_(2)=5(sin3pit+sqrt3cos3pit)`. What is the ratio of their amplitudes?

Explanation

The amplitude of the first SHM, `A_(1)=10`
Now, `y_(2)=5(sin3pit+sqrt3cos3pit)`
`=5xx2(1/2sin3pit+sqrt3/2cos3pit)`
`=10("cos"pi/3sin3pit+"sin"pi/3cos3pit)`
`=10sin(3pit+pi/3)`
`therefore` The amplitude of the second SHM, `A_(2)=10`
Hence, `A_(1)/A_(2)=10/10=1or,A_(1):A_(2)=1:1`.