Solving Mass Spring System Homework

[diracdelta]

Homework Statement

Starting from system of springs and masses (on picture), fina a force in x direction which n-th mass acts on n+1st mass, if harmonic wave ψ(x,t) is traveling in system.
In equilibrium every mass is compressed i acts with force of F₀ on masses.
Consider a case in boundary of continuum (a→0)
a is distance from first to next mass.

Homework Equations

Second Newton's law, F=m*a
ψ(x,t)= Asin(ωt -kx)

The Attempt at a Solution

Equation of motion for n-th mass:
md²x_n/dt²= k[(x_n+1-x_n) -n*a] -k(x_n - x_n-1)-n*a]

Analogous , for n+1 mass we have
md²x_n+1/dt²= k[(x_n+2-x_n+1) -n*a] -k(x_n+1 - x_n)-n*a]
Usually, we guess the soulution. For standard harmonic oscillator, it was x(t) = A cos (ωt + φ).
But now, there is also a wave in here. What to do with it?
What is his part in this problem?
Do i try to guess soultion also?
Should i try to find a force from as from above equations or somehow different?
What is phyisical meaning of " springs are in equilibrium and every spring is compressed and acts on mass with force of F0?
Does that withdraws an driven oscillator?

 

[Orodruin]

I suggest starting by replacing all of the xs by the sum of the equilibrium positions and the deviation from the equilibrium positions. This is what is going to be represented by your harmonic wave ψ.

 

[OldEngr63]

The information about F0 establishes a pre-load in the system. The equilibrium position has an amount of compression in the string equal to F0.

I suggest that you draw several FBDs and write the equations of motion for each mass, one by one, remembering that the springs are pre-loaded.