Question

A particle is subjected to two parallel S.H.M.s such that x = 2 sin ωt and y = `2 sin (omega t + pi/3)`. The amplitude of the resultant S.H.M. will be ______.

Options

• 0

• `2 sqrt 3`

• 4

• 12

Answer 1

A particle is subjected to two parallel S.H.M.s such that x = 2 sin ωt and y = `2 sin (omega t + pi/3)`. The amplitude of the resultant S.H.M. will be `bbunderline(2 sqrt 3)`.

Explanation:

Given: x = 2 sin⁡ ωt

y = `2 sin (omega t + pi/3)`

A₁ = A₂ = 2

Phase difference (ϕ) = `pi/3`

Resultant amplitude formula:

A = `sqrt(A_1^2 + A_2^2 + 2A_1A_2 cos phi)`

= `sqrt((2)^2 + (2)^2 + 2 (2) (2) cos (pi/3))`

= `sqrt(4 + 4 + 8 xx 1/2)`

= `sqrt(8 + 4)`

= `sqrt 12`

= `2 sqrt 3`