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The displacement of a particle varies with time according to the relation `y=a sin omega t +b cos omega t `.A. The motion is oscillatory but not S.H.M.B. The motion is S.H.M. with amplitude `a+b`C. The motion is S.H.M. with amplitude `a^(2)+b^(2)`.D. The motion is S.H.M. with amplitude `sqrt(a^(2)+b^(2))` |
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Answer» Correct Answer - D `Y=asinomegat +bcosomegat` …(i) Let `a=Acostheta` and `b=Asintheta` Then `a^(2)+b^(2)=A^(2)(cos^(2)theta+sin^(2))A^(2)` or `A=sqrt(a^(2)+A^(2))` From (i), `y=A costheta sinomegat+Asintheta cosomegat=Asin(omegat+theta)` It is an equation of SHM with amplitude `A=sqrt(a^(2)+b^(2))` |
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