the title is how to combine two vibration in two dimension at right angles w1 don t equal to w2

if o = pi/4 and x= A1 cos (w1t)
y= A2 cos (w2t+pi/4)

please give the method to how can you draw at the right angle this vibration and thanks .

 

The method is to eliminate time, t by combining the expressions to leave a single expression in x and y.

This expression is the locus of a point in the xy plane which is described by the combined motion.

Since you haven't stated any relation between w1 and w2 I can't be more specific. If the ratio of w1 to w2 is a whole number, the motion describes Lissajous figures which form recognizable regular patterns.

 

thank you for the reply 'studiot' and the relation betwwen w1 and w2 is w2=2w1 but for the lissajous figure it is easy to find it if w1=w2 but here it's not the case beause w2=2w1 which make the x and y independente equation and if we use trigonometric relation it will gonna be more harder ^^.