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Aman Deep Singh Grade: 12
        

IF WE ARE GIVEN WITH TWO OR MORE DISPLACEMENT EQUATIONS OF   S.H.M OF FORM


y=Asin(wt+kx+phase angle)


THEN HOW TO FIND RESULTANT AMPLITUDE,PHASE ANGLE

7 years ago

Answers : (2)

Badiuddin askIITians.ismu Expert
147 Points
										

Dear Aman


let


y1=A1sin(wt+kx)


y2=A2sin(wt+kx+Φ)


y=y1 +y2


  =A1sin(wt+kx)  +  A2sin(wt+kx+Φ)


  =A1sin(wt+kx )  +A2sin(wt+kx)cos(Φ) +A2cos(wt+kx)sin(Φ)


  =(A1 +A2 cosΦ  )sin(wt+kx ) +A2cos(wt+kx)sin(Φ)


   let  (A1 +A2 cosΦ  ) =A cosδ


and A2 sinΦ  =Asinδ


so y= A cosδ sin(wt+kx ) +Asinδcos(wt+kx)


        =Asin(wt+kx+δ )


  here A is resultant magnitude and  δ is phase angle


A=(A12 +A22 +2A1A2cosδ)1/2


tanδ =A2sinΦ/(A1 +A2cosΦ)


 





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7 years ago
V.S.R Vijay
8 Points
										

Dear Aman


let


y1=A1sin(wt+kx)


y2=A2sin(wt+kx+Φ)


y=y1 +y2


  =A1sin(wt+kx)  +  A2sin(wt+kx+Φ)


  =A1sin(wt+kx )  +A2sin(wt+kx)cos(Φ) +A2cos(wt+kx)sin(Φ)


  =(A1 +A2 cosΦ  )sin(wt+kx ) +A2cos(wt+kx)sin(Φ)


   let  (A1 +A2 cosΦ  ) =A cosδ i don''t understand why??


and A2 sinΦ  =Asinδ i don''t understand why?? please help me! 


so y= A cosδ  sin(wt+kx ) +Asinδcos(wt+kx)


        =Asin(wt+kx+δ )


  here A is resultant magnitude and  δ is phase angle


A=(A12 +A22 +2A1A2cosδ)1/2


tanδ =A2sinΦ/(A1 +A2cosΦ)

3 years ago
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