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Question:

When two displacements represented by y1=a sin(ωt) and y2=bcos(ωt) are superimposed, the motion is:

simple harmonic with amplitude√a² + b²

not a simple harmonic

simple harmonic with amplitude ab

simple harmonic with amplitude (a+b)²

Solution:

yresultant = y1 + y2 = asin(ωt) + bcos(ωt) = asin(ωt) + bsin(ωt + π/2)
Thus, the displacements are at right angles to each other.
∴amplitude of yresultant is √a² + b²