Question

When two displacements represented by y₁ = a sin(ωt) and y₂ = b cos(ωt) are superimposed the motion is ______. 

Options

• not a simple harmonic

• simple harmonic with amplitude `"a"/"b"`

• simple harmonic with amplitude `sqrt("a"^2 + "b"^2)`

• simple harmonic with amplitude `("a" + "b")/2`

Answer 1

When two displacements represented by y₁ = a sin(ωt) and y₂ = b cos(ωt) are superimposed the motion is simple harmonic with amplitude `sqrt("a"^2 + "b"^2)`

Explanation:

Amplitude of resultant S.H.M

R = `sqrt("A"_1^2 + "A"_^2 + 2"A"_1 "A"_2 cos 90°)` 

R = `sqrt("A"_1^2 + "A"_2^2)`

= `sqrt("a"^2 + "b"^2)`