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Homework Help: Solving for t in SHM (complex solution)

  1. Mar 5, 2008 #1
    Hey guys, this is my first post, I was hoping you all could offer some advice. I'm facing a problem involving free undamped SHM. Everything is working out well so far but I ran into a problem when trying to find t. Here's what I have:

    x(t) = -2/3cos10t + 1/2sin10t

    Now, if I want to find the times when x(t) = 0... how would I go about that? In a similar problem that only involved a single term, I was able to use cos^-1 to solve for t, but in this case would that still hold? Setting x(t) to 0 I get:

    0 = -2/3cos10t + 1/2sin10t

    But now I'm stuck.

    Any help would be greatly appreciated!
  2. jcsd
  3. Mar 5, 2008 #2


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    Hi mouser! Welcome to PF! :smile:

    Hint: how might you re-arrange this equation? :smile:

    [size=-2](if you're happy, don't forget to mark thread "solved"!)[/size]​
  4. Mar 5, 2008 #3

    If I rearrange it to be:

    2/3cos10t = 1/2sin10t

    4/3cot10t = 1

    3/4tan10t = 1

    tan10t = 4/3

    t = (tan^-1(4/3))/10

    The answer is incorrect. Did I make a mistake in that algebra? Thank you for your help!
  5. Mar 5, 2008 #4


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    Looks ok to me!

    Except you only have one solution … there should be infinitely many … what are the others? :smile:

    (What were you actually asked for? Was it the times, or the period?)
  6. Mar 5, 2008 #5
    The question was "at what time does the mass pass through the equilibrium position heading downward for the second time?"

    I just figured out where I went wrong. The answer I got previously was only partially correct. For the correct answer I added the value for one full period and it checks out! eureka!

    Thanks tiny-tim!
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