1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Mass spring system

  1. Dec 3, 2014 #1
    1. The problem statement, all variables and given/known data
    image001.gif
    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.

    2. Relevant equations
    Second Newton's law, F=m*a
    ψ(x,t)= Asin(ωt -kx)
    3. 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?
     
  2. jcsd
  3. Dec 3, 2014 #2

    Orodruin

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    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.
     
  4. Dec 3, 2014 #3

    OldEngr63

    User Avatar
    Gold Member

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Mass spring system
  1. Mass spring system (Replies: 2)

  2. Mass spring system (Replies: 7)

Loading...