Question

Two parallel SHMs have equations y₁ = a₁ sin(ωt + 2π) and y₂ = a₂ sin(ωt + 4π). The amplitude of the resultant is ______

Options

• ±(a₁ + a₂)

• ±(a₁ - a₂)

• `sqrt(a_1^2 + a_2^2 + a_1a_2)`

• `sqrt(a_1^2 + a_2^2)`

Answer 1

Two parallel SHMs have equations y₁ = a₁ sin(ωt + 2π) and y₂ = a₂ sin(ωt + 4π). The amplitude of the resultant is ±(a₁ + a₂).

Explanation:

Two equations are

y₁ = a₁ sin(ωt + 2π) and

y₂ = a₂ sin(ωt + 4π).

The phase difference Φ = 4π - 2π

Resultant amplitude = `sqrt(a_1^2 + a_2^2 + 2a_1a_2)`

= `sqrt(a_1^2 + a_2^2 + 2a_1a_2 cos2pi)` = ±(a₁ + a₂)