# Two mass spring system - Correct ODE

I would like to study a two mass-spring system, considering also the gravity forces. I have this system: Figure 1

So, I took the equations from this site: http://scipy.github.io/old-wiki/pages/Cookbook/CoupledSpringMassSystem

And I put the masses in a vertical position and I considered these equations: $$m_1 x_1'' = m_1 g + k_2\cdot (x_2 - x_1 - L_2) - k_1\cdot(x_1-L_1) - c_1x_1'$$ $$m_2 x_2'' = m_2 g + F - k_2\cdot (x_2 - x_1 - L_2) - c_2 x_2'$$

With L1 and L2 the lengths of the springs when subjected to no external forces, and F the applied force.

Then I plot the positions: Figure 2

And I think it's weird because, in reality, the two masses must continuously going down, but as you can see in the graph, they are oscillating around their initial position.

What did I forgot? Thank you!

• 1) either wait longer or 2) make your $c_1, c_2$ larger so that the system will die down quicker (the $c_1, c_2$ controls how fast energy is leaving the system) – achille hui Apr 22 '18 at 16:48
• $F\,\hat{y}$ is a Constant Force such that it can be equilibrated by the springs. Indeed, you can write a simpler equation if you rewrite your equations around the equilibrium positions. Oscillations occurs around that position. – Felix Marin Apr 22 '18 at 18:00