## Physics, Superballs, and the RLC Circuit!

If you bounce a superball it might bounce pretty high on the way up, but it won’t quite make it to the top.

A spring also experiences resistance and in a circuit it is blatantly labeled “resistance.”

Therefore an RLC circuit will experience damped harmonic motion.

An RLC circuit can still be quite useful though, one case in which they are used is in radio receivers.

If the capacitance is adjusted then the natural frequency will change and the amplitude will increase greatly for a certain frequency (similar to how a swing increases distance with a certain frequency).

## LRC Circuit, Differential Equations, and an Easier Approach – Phaser Diagrams

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.