DEQ/Algebra Question Solve for t

[Fish Sauce]

Solved: DEQ/Algebra Question Solve for t

Homework Statement

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.

Homework Equations

$\frac{\sqrt{31}}{150}=e^{-2t}\sin(2\sqrt{31}t)$

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.
$\ln{\frac{\sqrt{31}}{150}}=-2t+\ln(\sin(2\sqrt{31}t))$

Any help is greatly appreciated.

 

[LCKurtz]

Homework Statement

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.

Homework Equations

$\frac{\sqrt{31}}{150}=e^{-2t}\sin(2\sqrt{31}t)$

The only way to solve that for t would be numerically.

 

[Fish Sauce]

The only way to solve that for t would be numerically.

Thank you LCKurtz.

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

Thanks again!