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```				   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

Share

```										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
```										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??
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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