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Homework Help: Need help with finding positive time for x(t)= cos(wt) + sin(wt) problem

  1. Feb 27, 2012 #1
    1. The problem statement, all variables and given/known data

    This is for a physics class but at this point in the problem it's basic math... which for some reason I can just not figure out. I need to find at what time x(t) = 0 and I keep getting the negative time... I want the first positive time.

    2. Relevant equations

    x(t) = 3cos(10t) + 5sin(10t) = 0

    3. The attempt at a solution

    i get that t = [itex]\frac{arctan(-3/5)}{10}[/itex] which equals -0.054 seconds. Since you can't really have negative time the answer should be 0.26 seconds which is shown if this equation is graphed. I know this is dumb but I cannot figure out how to get this answer. I'm pretty sure you just have to shift it a certain amount... I just don't know what that amount is :/
  2. jcsd
  3. Feb 27, 2012 #2


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    Homework Helper

    Re: Harmonic Oscillation... just a simple math issue

    If you write it as z = 3*cos(A) + 5*sin(A) = 0
    and do the old transformation method for solving trigonometric equations: x = cos(A), y = sin(A) it becomes 3x + 5y = 0. This represents a line on the graph, and the intersections of the line with the unit circle are the solutions. Clearly there are two solutions for A, one positive and one negative.
  4. Feb 27, 2012 #3


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    Gold Member

    The general solution to the equation, [itex]\tan(x)=A\,,[/itex] is [itex]x=\arctan(A)+k\pi\,,[/itex] where k is an integer.
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