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

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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`

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Solution

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)`

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