spring.lua

local RunService = game:GetService("RunService")
local ReplicatedStorage = game:GetService("ReplicatedStorage")

local character = script.Parent
local springModel = ReplicatedStorage.spring

springModel.Parent = workspace

local current = springModel.Current
local goal = springModel.Goal

local velocityAngle = 0
local velocityAxis = Vector3.new(1,0,0)

local stiffness = 3
local damping = 1

function stepSpring(dt)
	local currentOrientation = current.CFrame - current.CFrame.p
	local goalOrientation = goal.CFrame - goal.CFrame.p
	
	local offset = goalOrientation:inverse() * currentOrientation
	local offsetAxis, offsetAngle = offset:ToAxisAngle()
	
	-- hookes law: F = -kx - bv
	-- if you know lots of cool calculus you can do some
	-- differential equations and get this as a function 
	-- of dt but im bad at math and dont know how that works :(

	local force = -stiffness * offsetAngle
	force = force - (velocityAngle * damping * (1/dt))
	
	
	local dt_acceleration_mat = CFrame.fromAxisAngle(offsetAxis, force * dt)
	
	local dt_velocity_mat = CFrame.fromAxisAngle(velocityAxis, velocityAngle) * dt_acceleration_mat
	velocityAxis, velocityAngle = dt_velocity_mat:ToAxisAngle()
	
	current.CFrame = current.CFrame * dt_velocity_mat
end