Question

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

पर्याय

• ±(a₁ + a₂)

• ±(a₁ - a₂)

• ${\displaystyle \sqrt{a_1^2+a_2^2+a_1{a}_2}}$

• ${\displaystyle \sqrt{a_1^2+a_2^2}}$

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 = ${\displaystyle \sqrt{a_1^2+a_2^2+2a_1{a}_2}}$

= ${\displaystyle \sqrt{a_1^2+a_2^2+2a_1{a}_2\cos 2\pi }}$ = ±(a₁ + a₂)