Mass-Spring-Damper
This script plots a solution for the dampened mass-spring system using a simple Euler method. The second degree ODE has to be modified into two first order ODEs.
d²x/dt²+ 2*ζ*ωn*dx/dt + ωn²*x = 0
v = dx/dt
=> dv/dt + 2*ζ*ωn*v + ωn²*x = 0
=> dv/dt = -2*ζ*ωn*v - ωn²*x
dx/dt = v
ωn = sqrt(k/m)
ζ = c/(2*m*ωn)
- Undamped systems ζ = 0
- Underdamped systems ζ < 1
- Critically damped systems ζ = 1
- Overdamped systems ζ > 1
The script uses matplotlib for plotting.