Differential Equations

For my final project in my Differential Equations class, I decided to write a paper on RLC series circuits using LaTeX in Overleaf. An RLC circuit can be thought of as a spring mass damper. The capacitor acts as the spring: It opposes changes in voltage which can be the position. The inductor acts as the mass, as it opposes changes in current, which can be thought of as the velocity. The resistor acts as the damper, as it dissipates energy through a voltage drop similar to friction. If you removed the resistor, the circuit would become an oscillator, which would oscillate forever using idealized components. I analyzed the homogeneous, which is known as the transient, and the particular, steady state, solutions which sum into the total solution to the differential equation.