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Homework Help: Free vibrations question

  1. Dec 9, 2014 #1
    I know this question has already been asked, but the given answer di not help me. Hopefully someone can post their full solution?

    A piston of mass 4.53(kg) is travelling in a tube with a velocity of 15.24(m/s). It engages a spring of stiffness 350 (N/cm) and a damper with a coefficient of 1.75 (N.s/cm)

    What is the maximum displacement of the piston and how long does it take to reach this point?

    2. Relevant equations
    F= -kx
    x is the displacement vector - the distance and direction in which the spring is deformed
    F is the resulting force vector - the magnitude and direction of the restoring force the spring exerts
    k is the spring constant or force constant of the spring.


    Damping : http://en.wikipedia.org/wiki/Damping

    3. The attempt at a solution
    I have the solutions, Max. Displacement = 128.6(mm), Time Taken = 0.0157(s). I am stuggling to find a link between the known data and the displacement. Hope you can help
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Dec 9, 2014 #2


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    Staff: Mentor

    Hi Lukergr. http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif [Broken]

    The damper resists with a force proportional to velocity, with units N per m/s, written F=-k.x' so it's a 2nd order differential equation you'll be looking to solve. Motion of the piston is resisted by both the spring and the damper. You'll find a worked example in almost every textbook on physics or calculus 101.
    Last edited by a moderator: May 7, 2017
  4. Dec 9, 2014 #3


    User Avatar
    Gold Member

    Is this a diff eq based course?
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