1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    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!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Calculus Logarithmic Functions help please
  1. CAlculus help please (Replies: 3)

Loading...