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DEQ/Algebra Question Solve for t

  1. Jul 22, 2011 #1
    Solved: DEQ/Algebra Question Solve for t

    1. The problem statement, all variables and given/known data
    Greetings,

    I am having difficulty solving for t in the equation below. It is part of a DEQ question that asks at which time t does damped oscillation amplitude fall below a certain value. The relevant equation is below. My main problem is that I am having difficulty solving for t since t is a product of e and the sin function.


    2. Relevant equations
    [itex]
    \frac{\sqrt{31}}{150}=e^{-2t}\sin(2\sqrt{31}t)
    [/itex]


    3. The attempt at a solution
    Trying to take ln of both sides produces the following, which I am still at a loss as how to solve for t.
    [itex]
    \ln{\frac{\sqrt{31}}{150}}=-2t+\ln(\sin(2\sqrt{31}t))
    [/itex]

    Any help is greatly appreciated.
     
    Last edited: Jul 22, 2011
  2. jcsd
  3. Jul 22, 2011 #2

    LCKurtz

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    Science Advisor
    Homework Helper
    Gold Member

    The only way to solve that for t would be numerically.
     
  4. Jul 22, 2011 #3
    Thank you LCKurtz.

    I thought I was overlooking a simple algebraic solution and was losing hair over this!

    Thanks again!
     
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