/gist:32adced1e5589b3e244b Secret

## gistfile1.txt
Such a system obeys Hooke's law, F(x) = -kx, which produces a simple sinusoidal wave x = Acos(⍵t+𝜙).
What happens when you grab the wagging tail? You create a system that's a variation of the driven damped harmonic oscillator.
Ignoring the damping for a moment, grabbing the tail very firmly is basically applying a driving force to the tail, equal to the inertia of the object grabbing it. Basically, I'm ignoring muscle movements, and just pretending that a weight is glued to the tail. Because inertia produces a force proportional to the acceleration, we can model F(t) with that.
This means we get the equation (∂^(2)x/∂t^(2)) + ⍵^(2)x = F(t)/m(obj)
I think I fucked up on my math somewhere because I feel like I'm missing a c(∂x/∂t) somewhere, but it's been a few years since I took diffeq. You should end up with a damped wave, but this current equation also produces a sinusoidal wave, but smaller by 1/(F/m).
	Such a system obeys Hooke's law, F(x) = -kx, which produces a simple sinusoidal wave x = Acos(⍵t+𝜙).
	What happens when you grab the wagging tail? You create a system that's a variation of the driven damped harmonic oscillator.
	Ignoring the damping for a moment, grabbing the tail very firmly is basically applying a driving force to the tail, equal to the inertia of the object grabbing it. Basically, I'm ignoring muscle movements, and just pretending that a weight is glued to the tail. Because inertia produces a force proportional to the acceleration, we can model F(t) with that.
	This means we get the equation (∂^(2)x/∂t^(2)) + ⍵^(2)x = F(t)/m(obj)
	I think I fucked up on my math somewhere because I feel like I'm missing a c(∂x/∂t) somewhere, but it's been a few years since I took diffeq. You should end up with a damped wave, but this current equation also produces a sinusoidal wave, but smaller by 1/(F/m).