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when two displacements represented by `y_(1) = a sin(omega t)` and `y_(2) = b cos (omega t)` are superimposed the motion isA. simple harmonic with amplitude `(a)/(b)`B. simple harmonic with amplitude `sqrt(a^(2)+b^(2))`C. simple harmonic with amplitude`((a+b))/(2)`D. not a simple harmonic |
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Answer» Correct Answer - B Here, `y_(1)=a sin omegat ` and `y_(2)=b cos omega t =b sin (omegat+(pi)/(2))` `A_(1)=a, A_(2)=b, phi=pi//2`j Since the frequencies of both the displacements are same, resusltant motion will be SHM. No amplitude `A=sqrt(A_(1)^(2)+A_(2)^(2)+2A_(1)A_(2)cosphi)`. `:. A=sqrt(a^(2)+b^(2))` |
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