Two particles executing simple harmonic motion as described by `y_1 = 30 sin (2 pi t + pi /3 )` and `y_2 = 10 ( sin 2pi t + sqrt(3) cos 2pi t )` have amplitudes `A_1` and `A_2` respectively. The ratio ` A_1 : A_2` is

Options

A. `2:1`
B. `1:1`
C. `3:1`
D. `1:sqrt3`

Answer

C

Explanation

Given,
Two particles execute S.H.M
`y _(1) = 30 sin (2 pi t + (pi)/(3))`
Here,
`A _(1) = 30m`
`y_(2) = 10 ( sin 2 pi t + sqrt3 cos 2 pi t )`
`implies y_(2) = 10 xx 2 ((1)/(2) sin 2 pi t + (sqrt3)/(2) cos 2pi t )`
`=20(cos ""(pi)/(3) sin 2 pi t + sin ""( pi)/(3) cos 2 pi t)`
`= 20 sin ( 2 pi t + (pi)/(3))`
Here,
`A _(2) = 20`
` A _(1) : A _(2) = 30 : 20`
` = 3:2`
`therefore A _(1) :A_(2) = 3:2`