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Homework Help: Calculus Logarithmic Functions help please

  1. Aug 2, 2010 #1
    Calculus Logarithmic Functions help please!!

    The question is:
    A particle moves alonge the x-axis with position at time t given by x(t) = e^(-t) sin t for 0 ≤ t ≤ 2π.

    1. Find the time t at which the particle is farthest to the left. Justify your answer.
    2. Find the value of the constant A for which x(t) satisfies the equation
    Ax" (t) + x' (t) + x(t) = 0 for 0 < t < 2π.

    For no.1, I think its when t=0, because within the interval 0 ≤ t ≤ 2pi, 0 is when x has the least value, therefore most to the left.

    For no.2, x(t)= e-t sin t, x'(t)= e-t (cos t - sin t), and x''(t)= -2e-t cos t. Factorizing, x(t)+x'(t)+x''(t) gives me e-t (sin t +cos t -sin t -2A cos t). To make the sums inside parentheses zero, A would have fit the condition 0= cos t - 2A cos t. A= [tex]\frac{1}{2}[/tex] fits, it seems.

    Am I on the right track? Thanks
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Aug 2, 2010 #2

    Filip Larsen

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    Gold Member

    Re: Calculus Logarithmic Functions help please!!

    For 1: Is there a way you can check if x(t) is a minimum for t = 0? How would you normally find a minimum of x when you have access to the derivatives x' and x''?

    For 2: Looks correct.
  4. Aug 2, 2010 #3
    Re: Calculus Logarithmic Functions help please!!

    aah, i didn't think about that..thanks!
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