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Free Vibration- Viscous Damping

  1. Oct 7, 2011 #1
    1. The problem statement, all variables and given/known data

    Scenario 1: Mass suspended from dasphot (damper) and spring
    Mass=M
    Damping Coefficient=c
    Spring Constant=K

    Scenario 2: Mass supported by dashpot (damper) and spring
    Mass=M
    Damping Coefficient=c
    Spring Constant=K

    In both cases, derive the equations of motion assuming that each mass is at some point displaced from static equilibrium.

    Justify the use of positive or negative signs in the problem

    2. Relevant Concepts
    D'almbert's principle
    Fspring= -kx
    Fdamping= cx'

    3. The attempt at a solution

    Sign Conventions are throwing me for a loop. The equation will in both cases be of the form:
    mx"+cx'+k(deltastatic+x)=weight

    solutions will be of the form:
    x(t)=Ae^(a+lamda*i)t + Be^(a-lambda*i)t


    BUT HOW DO I JUSTIFY THE SIGN CONVENTIONS!? Free body diagrams are really confusing me in what is a relatively simple problem
     
  2. jcsd
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