(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Homework Help: DEQ/Algebra Question Solve for t

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