Two simple harmonic motions are represented by `y_(1)=5[sin2pit+sqrt(3)cos2pit]` and `y_(2)=5sin(2pit+(pi)/(4))` The ratio of their amplitudes is

Options

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

Answer

B

Explanation

`y_(1)=5[sin2pit+sqrt(3)cos2pit]`
`=10[1/2sin2pit+(sqrt(3))/(2)cos2pit]`
`=10["cos"(pi)/(3)sin2pit+"sin"pi/3cos2pit]`
`=10["cos"pi/3"sin2pit+"sin"(pi)/(3)cos2pit]`
`=10[sin(2pit+(pi)/(3))]`
`:.A_(1)=10`
`y_(2)=5sin(2pit+(pi)/(4))`
`:.A_(2)=5`, Hence `(A_(1))/(A_(2))=(10)/(5)=(2)/(1)`