When two displacements represented by $straight y subscript 1 space equals space straight a space sin space space left parenthesis ωt right parenthesis space and space straight y subscript 2 space equals space straight b space cos space left parenthesis ωt right parenthesis$ are superimposed, the motion is

not a simple harmonic

simple harmonic with amplitude a/b

simple harmonic with amplitude $square root of straight a squared plus straight b squared end root$

simple harmonic with amplitude $fraction numerator left parenthesis straight a plus straight b right parenthesis over denominator 2 end fraction$

Solution

simple harmonic with amplitude $square root of straight a squared plus straight b squared end root$

straight y subscript 1 space equals space straight a space sin space ωt straight y subscript 2 space equals space straight b space cos space ωt space equals space straight b space sin space open parentheses ωt space plus straight pi over 2 close parentheses The space resultant space displacement space is space given space by space straight y equals straight y subscript 1 space plus straight y subscript 2 space equals space square root of straight a squared plus straight b squared end root space sin space left parenthesis ωt space plus straight ϕ right parenthesis Hence comma space the space motion space of space superimposed space wave space is space simple space harmonic space with amplitude space square root of straight a squared plus straight b squared end root

Some More Questions From Mechanical Properties of Fluids Chapter

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