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Homework Help: Mechanics Vibrations

  1. Aug 29, 2010 #1
    1. The problem statement, all variables and given/known data
    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
    where
    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.

    velocity=displacement/time

    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. Aug 30, 2010 #2
    Integrate the wikipedia equation with the conditions x(0)=0, v(0)=15.24 (cauchy problem); the system is underdamped, you will find a solution like exponential*sin, for the maximum displacement set the condition v(t)=0, i found it at t=0.01572s, if you want further help i can give you the analytic solution but i'm not good at Latex, it's more like a math exercise than a physic's one
     
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