No problem! I'm glad that helped, because I haven't used phasors since learning them a few semesters ago, and I wouldn't have been able to make many more useful observations in my sleep-deprived state [emoji14]
It's like counting people with your fingers; you are representing each person with a finger, because math works similarly for both fingers and people, but fingers are more convenient.
Or maybe I should sleep.
For a rigorous proof, we need a precise question.
The units of P_0 are clearly volts, so that much is self-evident. It is also evident that if V_0=Re[P_0e^{jwt}] and V_1=Re[P_1e^{jwt}], then V_0+V_1=Re[P_0e^{jwt}]+ Re[P_1e^{jwt}]=Re[(P_0+P_1)e^{jwt}].
What do you want to prove?
They do not represent the same quantity, even though they represent the same concept. It is an error to equate both to V; my book used v (lower case) for the time-domain value, and V (capital) for the phasor (or "frequency") domain value. The units are the same, but the values are not!
The...
I hate to make a request when this semester has had me too busy to be active here, but... since you were so kind to send me Foundation, I think the Prelude to Foundation would go nicely with it. Both with make good summer reading while I'm out of town for an internship and free from classes :)
Edit: I forgot to add the picture, and I'm having trouble adding it from Tapatalk. I'll add it soon.
I'm trying to understand the derivation in my textbook of the wave function for a potential step. The derivation reaches the step shown in the attached photo, which I am fine with.
However, the...
Ah, I guess I had no idea what kind of output an accelerometer produces. I thought that 0 would also be the "rest" value, resulting in no net change when falling.