Solving for time with an Overdamped Oscillator

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SUMMARY

The discussion focuses on solving for time (t) in the context of an overdamped oscillator described by the equation x(t) = A1*e^-(γ-q)*t + A2*e^-(γ+q)*t. The specific parameters provided are A1 = 3.61, A2 = -0.61, γ = 0.9, and q = 0.64. The goal is to determine when the mass is within 10% of its equilibrium position, calculated as 0.3m. The user encountered difficulties in isolating t due to its presence in two exponential terms, leading to an equation that resulted in negative values for time, which is not physically meaningful.

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Homework Statement


How long will it take until the mass is within 10% of its equilibrium?

I already solved most of what is needed in previous parts of the question. I just need help solving for t because it is in two exponents in the equation.


Homework Equations


This is the equation
x(t) = A1*e-(γ-q)*t + A2*e-(γ+q)*t
A1 = 3.61
A2 = -0.61
γ = 0.9
q = 0.64

The Attempt at a Solution


First I found where x is .1 from its equilibrium
x = .1A = .1(3m) = 0.3m
Then I plugged in the A values. I divided the right side of the equation by x and moved the whole A2 term to the left of the equation to have an exponential on both sides.
Then I took the ln of both terms to have an equation with t on both sides.
-(γ+q)*(A2/x )*t = -(γ-q)*(A1/x)*t

If I plug these variables in, I am left with
number*t = number*t and that isn't really solvable...
 
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Everytime I come up with an answer, it is negative but time can't be..
 

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