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Lightly damped spring system Q

  1. Mar 25, 2008 #1
    [SOLVED] Lightly damped spring system Q

    1. The problem statement, all variables and given/known data

    Consider a lightly damped mass-on-a-spring vibrational system. How should motion be initiated so that the amplitude of the spring is given by;

    [tex]\Psi(t)=Ce^{-\frac{\lambda}{2}t}Cos(\omega_{r}t+\pi)[/tex]

    2. Relevant equations



    3. The attempt at a solution

    I don't really know what is being asked "how should motion be initiated". Anyways I tried finding the solution at t=0,

    [tex]\Psi(0)=Ce^{-\frac{\lambda}{2}*0}Cos(\omega_{r}*0+\pi)[/tex]

    Which simplifys to [tex]\Psi(0)=-C[/tex] (as [tex]e^{0}=1[/tex] and [tex]Cos(\pi)=-1[/tex])

    So is my answer just the spring should be stretched by aplitude C to give above equation of displacement? Thanks.
     
  2. jcsd
  3. Mar 25, 2008 #2

    pam

    User Avatar

    Also find the initial velocity by d\psi/dt.
     
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