Does Phase Relationship Matter in AC Circuits and SHM?

[schaefera]

Let's focus specifically on AC circuits and a mass on a spring since those are the types of SHM I know.

Does the phase relationship matter? For instance, with a mass on a spring, position and velocity are 90 degrees out of phase. But does it matter to say which leads the other? After all, that seems like a matter of initial conditions that goes away after an oscillation.

For the AC circuit it seems a bit more important to say whether voltage leads or lags current, since it's not always that clean 90 degrees difference in phase. But does this have any physical meaning, whether it leads or lags an by how much?

I know that if we think of the voltage across each element in an RLC circuit as a vector rotating around the origin, then we can take the vector sum of those 3 vectors and compare it to the voltage across the resistor to see whether it leads or lags. But does that matter?

 

[tiny-tim]

hi schaefera!

Let's focus specifically on AC circuits and a mass on a spring since those are the types of SHM I know.

Does the phase relationship matter? For instance, with a mass on a spring, position and velocity are 90 degrees out of phase. But does it matter to say which leads the other? After all, that seems like a matter of initial conditions that goes away after an oscillation.

in shm, position and velocity will always be 90° out of phase

For the AC circuit it seems a bit more important to say whether voltage leads or lags current, since it's not always that clean 90 degrees difference in phase. But does this have any physical meaning, whether it leads or lags an by how much?

if it's not 90°, it's not shm

the phase difference matters because it alters the power (and also the power loss) …

instantaneous power = instantaneous current times instantaneous voltage ​

(it also matters because it tells you how to calculate the impedance if you join that circuit to another circuit)

 

[sophiecentaur]

Let's focus specifically on AC circuits and a mass on a spring since those are the types of SHM I know.

Does the phase relationship matter? For instance, with a mass on a spring, position and velocity are 90 degrees out of phase. But does it matter to say which leads the other? After all, that seems like a matter of initial conditions that goes away after an oscillation.

For the AC circuit it seems a bit more important to say whether voltage leads or lags current, since it's not always that clean 90 degrees difference in phase. But does this have any physical meaning, whether it leads or lags an by how much?

I know that if we think of the voltage across each element in an RLC circuit as a vector rotating around the origin, then we can take the vector sum of those 3 vectors and compare it to the voltage across the resistor to see whether it leads or lags. But does that matter?

It doesn't "matter". It just describes a set of relationships that is always there. There is a logic to the lagging and leading thing, though and it comes with the direction of the vectors which describe what's happening and the result of differentiating position - to give velocity and then velocity to give acceleration.

Take a mass on a spring when the mass has been stretched, prior to being let go. The position (displacement) is maximum negative, the force (and hence the acceleration) is maximum positive and the velocity, after you let go is zero but increasing in the positive direction. As you pass the equilibrium point, the displacement is zero, the acceleration is zero and the velocity is maximum positive. etc etc
If you actually scribble a diagram of this, putting the sinusoids one above the other with the same time scale (carefully: I can't guarantee a scribble on the screen would be convincing but you can take several goes to make it right), you will see the phases of the sinusoidal variation of position, velocity and acceleration. There is a lag between each of a quarter of a cycle.
PS No need to draw it out. It's on this link that I just found, complete with animation.