Lissajous pattern

Hi guys,

Is there anybody to let me know why does the Lissajous pattern of a circuit/ component become a line with an angle of 45 degrees (it is observed while putting the scope in X-Y mode)? I expect it to be line with an angle of 0 degree (straight line). But can not find any formula or function for 45 degrees of variation while we have a pure resistance.

Any help is welcomed.

Thanks

Another question is that I noticed that putting a scope in x-y mode and then measuring Lissajous pattern results an accurate result than measuring it by scope while is in normal mode (mot in X-Y mode). Do you know what's the reason?
For instance while I wanted to measure the resonance frequency of an speaker I noticed a 1kHz difference between measuring it by scope in normal mode and in x-y mode, while the normal mode gave me a precise result than X-y mode.

In answer to your first question a 45 degree line is the result of applying the same voltage to both the X and the Y inputs.
Re your second question, how are you measuring resonance frequency? What are the X and Y signals?

Graduate both axis with same values (whatever) plot the intersection pairs. Bet it is a straight line.