math math math
Now, instead of solving equations to find numbers, i solve equations to find more equations.
i.e.
shows various solution curves for the expression x'' + 2x' +26x = 82cos(4t). this looks simple, but after solving for x it looks like x(t)=exp(-t)*[(x0-5)*cos(5*t)+1/5*(x0-21)*sin(5*t)] +5*cos(4*t) +4*sin(4*t). These equations are a bitch to solve, basically.
If that werent fun enough, im also enrolled in a lab where we make computer models of these things. good times.
here is a model i made of a damped, driven oscillator:
here is a plot I made to show what happens to oscillation amplitude as drive frequency increases. the spike is where the natural frequency nears the drive frequency, and is called resonance.
edit:
here are some sweet markov-chain-ish plots that i made.
