Solving for time with an Overdamped Oscillator

  • Thread starter Thread starter NewtonsHead
  • Start date Start date
  • Tags Tags
    Oscillator Time
Join the discussion
Registration is free. Ask a follow-up in this thread, or start your own.
1 reply · 2K views
NewtonsHead
Messages
26
Reaction score
0

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...
 
Physics news on Phys.org
Everytime I come up with an answer, it is negative but time can't be..