2 degree of freedom system modeling

[omka]

Hello,
I'm having difficulty finding equation of motion for 3 degree of freedom spring mass system.

Homework Statement
the positions of the masses at the equilibre are respectively X10, X20, X30
At t = 0s, the mass m1 is drawn to the left with the force T (t).
Each of the masses is moved from it's equilibrium position by x1 (t), x2 (t) and x3 (t), respectively.
Write the fundamental equation of the dynamics for m1, m2 and m3
K1 stiffness coefficient spring 1
K3 stiffness coefficient spring 2
f1 f2 f3 viscous coefficient

Homework Equations

the fundamental equation of the dynamics

The Attempt at a Solution

At t= 0s When the mass m1 has moved a distance x1 from it's position (to the left) the spring k1 will be stretched that mean that this spring will be exerting a force on the mass to the right. The viscous force f1 will be exerting also a force on the right because the viscous fiction is always opposite to the direction of motion.

But the motion of m1 depend also of the motion of mass 2 and so of f2.
Could you please help me to understand what are the forces exerted on the mass 1 and mass 2 from the other masses.

 

[DrClaude]

I'm having difficulty finding equation of motion for 2 degree of freedom spring mass system.

Doesn't the picture show 3 degrees of freedom?

When the mass m1 has moved a distance x1 from it's position the spring k1 will be stretched that mean that this spring will be exerting a force on the mass to the right.

From the point of view of particle 1, does it matter if it is being pulled by the spring because particle 1 has moved to the left or because particle 2 has moved to the right?

Could you please help me to understand what are the forces exerted on the mass 1 from the other masses.

To be clear: it is not the other masses that exert forces, only springs and dampers.

 

[omka]

From the point of view of particle 1, does it matter if it is being pulled by the spring because particle 1 has moved to the left or because particle 2 has moved to the right?

This is my problem.i can't understand how can one mass move while the other is held still. if i apply force T(t)on m1 m2 will move too ?

 

[DrClaude]

This is my problem.i can't understand how can one mass move while the other is held still. if i apply force T(t)on m1 m2 will move too ?

The fact that the motion of the masses will be coupled is taken care of by the fact that you will get a set of coupled equations of motion. From the point of view of a mass, all that is important is the force acting on it.

So, given the position of the masses, what is the force on mass 1 due to k₁ and f₁?