Solving the General Solution for a Heavily Damped Oscillator

[Bonnie]

Homework Statement

The question I am working on is number 3 in the attached file. There are two initial conditions given: at time = 0, x(t) = D and x'(t) = v 'in the direction towards the equilibrium position'. Does that last statement mean that when I substitute the second IC in, I should enter it as x'(t) = - v instead of (+) v?

Homework Equations

The Attempt at a Solution

 

[Orodruin]

Yes. Your initial condition is not x'(0) = v, it is x'(0) = -v. (Assuming that D is positive.)

 

[Bonnie]

Thank you!