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diracdelta
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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:
md2xn/dt2= k[(xn+1-xn) -n*a] -k(xn - xn-1)-n*a]
Analogous , for n+1 mass we have
md2xn+1/dt2= k[(xn+2-xn+1) -n*a] -k(xn+1 - xn)-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?