An LRC circuit can be described by a second order differential equation, which in truth would take a long time to solve!
However, we also know that since each part is in series then the current will be the same throughout the circuit.
When we project the A onto the y-axis we get a and this functions like a cosine and/or sine.
We can then use “phaser diagrams” for the process.
There will be three different stages in the circuit and since the currents are lined up then the diagrams can be lined up accordingly and added vectorially.