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IF TWO OR MORE SHM EQUATIONS ARE GIVEN OF THE FORM y=Asin(wt+kx) SUCH THAT THE w i.e the angular freq. ARE DIFFERENT IN BOTH THEN HOW TO FIND RESULTANT w.

IF TWO OR MORE SHM EQUATIONS ARE GIVEN OF THE FORM


y=Asin(wt+kx)


SUCH THAT THE w i.e the angular freq.      ARE DIFFERENT IN BOTH THEN HOW TO FIND RESULTANT w.

Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

Dear Aman

y1=A'sin(w1t+kx)    &  y2=A'sin(w2t+kx)

y1 +y2 =A'sin(w1t+kx)    + A'sin(w2t+kx)

              =A'2cos(w1-w2)t/2 sin{(w1+w2)t/2 +kx}

     let |w1-w2|=δw     and (w1+w2)/2  =w

            y  =2A'cosδwt/2 sin(wt+kx)

                  =Asin(wt+kx)

 where A=2A'cosδwt/2


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Badiuddin


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