The ratio of amplitudes of two simple harmonic motions represented by the equations `y_(1) = 5 " sin" (2pi t + (pi)/(4) ) and y= 2 sqrt(2) ( sin 2pi t + cos 2pit )` is

Options

A. `1:1`
B. `2:1`
C. `5:2`
D. `5:4`

Answer

D

Explanation

Given, `y_1 = 5 sin (2pi t + (pi)/(4))`
`y _2 = 2 sqrt(2 ) ( sin 2pi t + cos 2pi t)`
Here, `A_1 =5 and A_2 = sqrt( (2 sqrt(2))^2 + (2 sqrt(2) )^2) `
`A_2 = sqrt( 8 + 8 ) =4`
Now, `(A_1)/(A_2) = (5)/(4)`