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. `3:2`
D. `1: sqrt3`

Answer

C

Explanation

displacement equation of the first particle,
`y_1 = 30 sin (2 pi t + pi/4)`
Hence, its amplitude, ` A_1 = 30 m `
displacement equation of the second particle,
`y_2 = 10 (sin 2pi t + sqrt(3) cos 2pi t)`
` = 10 xx 2 [ 1/2 sin 2 pi t + (sqrt3)/(2) cos 2 pi t]`
` = 20 [ cos pi/3 sin 2pi t + sin pi/3 cos 2 pi t ]`
` rArr y_2 = 20 sin (2 pi t + pi/3) `
` therefore` its amplitude , `A_2 = 20 m`
` therefore A_1 : A_2 = 30 : 20 = 3 : 2`