- #1

NewtonsHead

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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) = A

_{1}*e

^{-(γ-q)*t}+ A

_{2}*e

^{-(γ+q)*t}

A

_{1}= 3.61

A

_{2}= -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 A

_{2}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)*(A

_{2}/x )*t = -(γ-q)*(A

_{1}/x)*t

If I plug these variables in, I am left with

number*t = number*t and that isn't really solvable...