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!

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


    User Avatar
    Science Advisor
    Homework Helper

    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


    User Avatar
    Science Advisor
    Homework Helper

    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!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook