Transcript Superposition at right angles

Superposition at right angles
Vibrations having equal
frequencies.
Vibrations having different
frequencies.
Vibrations having equal
frequencies.
x  A1 sinωt  φ1 
y  A2 sinωt  φ2 
sin wt  φ  sin wt cos φ  cos wt sin φ
x
y
2xy
2
 2 
cos φ2  φ1   sin φ2  φ1 
2
A1 A2 A1A2
2
2
x
y
2xy
2
 2 
cos δ   sin δ 
2
A1 A2 A1A2
2
2
x
y
2xy
2
 2 
cosδ   sin δ 
2
A1 A2 A1A2
2
2
If  =  / 2
‫معادلة قطع ناقص‬
x
y
 2 1
2
A1 A2
2
2
If  =  / 2 , A1 = A2 =A
x y  A
2
2
2
‫دائرة‬
x 2 y 2 2xy
2
 2 
cosδ   sin δ 
2
A1 A2 A1A2
If  = o ,  ,2 , ..
x
y
2xy
 2 
0
2
A1 A2 A1A2
2
2
2
 x
y 

  0 

 A1 A2 
A2
y
x
A1
x
y

A1
A2
‫خط مسقيم‬
Vibrations having different
frequencies.