Simple problem: logarithmic decrement

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

    Note this is exam revision rather than actual course work worth marks, so there is no need to be deliberately vague :)

    The question comes in two parts, regarding a lightly damped harmonic oscillator with frequency 10 kHz and an amplitude that decays by 25% over 300 oscillations. First I am asked to calculate the logarithmic decrement, and then to make an expression that allows the amplitude to be calculated as a function of time elapsed.

    2. Relevant equations

    δ=(1/N)ln(A0/AN)

    3. The attempt at a solution

    The log decrement is 9.59x10-4. Easy. For the second part, simply rearranging the log decrement formula gives AN=A0e-Nδ. Knowing that N = 10,000*t, I get A(t)=A0e-9.59t.

    What I do not understand is why my course notes give A(t)=e-9.59t. Why is this answer not multiplied by A0? Mathematically and physically, this does not make sense to me - the amplitude as a function of time definitely does depend on the initial amplitude! Am I right in thinking that is a mistake?

    Thanks!
     
  2. jcsd
  3. diazona

    diazona 2,156
    Homework Helper

    Yes, you're right. If nothing else, the units don't match, that tells you the formula in your notes can't be correct.
     
  4. Ah good, thanks for confirming that!
     
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