Spring Mass and Oscillation Graphing and Simulator

Mass-spring systems are governed by the following differential equation. Play with the variables or drag the mass itself!

mx′′ + bx′ + kx = f(t)

	`m` = kg mass: resistance to force
	`b` = kg/s damping coefficient: resistance to movement
	`k` = kg/s² spring constant: stiffness of spring
	`f`(`t`) = `F`₀ cos `ωt` = kg px/s² forcing function: external force on block turn oscillation on \| reset `f`(`t`) = 0
	`ω` = s⁻¹ angular frequency of forcing function

We can find more information by rewriting the equation as:

x′′ + 2ζω₀x′ + ω₀²x = f(t) / m

	`ζ` = `b` / 2√`mk` = damping ratio: system is underdamped if 0 < `ζ` < 1 system is critically damped if `ζ` = 1 system is overdamped if `ζ` > 1
	`T` = 2π / `ω`₁ = s period of motion
	`ω`₀ = √`k / m` = s⁻¹ natural angular frequency: undamped frequency
	`ω`₁ = `ω`₀√1 - 2`ζ`² = s⁻¹ actual angular frequency (`ω`₀ ≈ `ω`₁ for `ζ` ≪ 1)