Equations of motion for a three-mass spring system using Newton's laws

[quasar987]

I have to find the equations of motion using Newton's laws for this system (see attached file). I have found them using Lagrange's equations and compared with a friend's results: we have the same.

$$m_1 (\ddot{x_1} - \ddot{x}) + k_1 x_1 = 0$$

$$m_2 (\ddot{x} + \ddot{x_2}) + k_2 x_2 = 0$$

$$m_1(\ddot{x} - \ddot{x_1}) + m_2 (\ddot{x} + \ddot{x_2}) + m_3 \ddot{x} = 0$$


But how do we arrive to that with Newton's laws? Why isn't it simply $m_1 \ddot{x_1} + k_1 x_1 = 0$ for $m_1$ ?!


eee.. I should have posted this in the homework help section, I apologize.

 

[quasar987]

I found the third one; it's the equation of motion for the center of mass of the system.

 

[quasar987]

And the other 2 work too if you consider the position of m1 and m2 as being mesured from the same axe as the position of m3 (i.e. the coordinate x) and take care of inverting the sign of the force on m1 because the x1 coordinate is measured in the opposite direction to x.

(I'm writting this because a lot of people have checked the thread but no one answered. So some people may be interested in the solution.)