1. The problem statement, all variables and given/known data The shock absorber of a car has elastic constant k. When the car is empty, the design is such that the absorber is critically damped. At time t=0 the absorber is compressed by an amount A from its equilibrium position and released. a) If after 1 second the absorber compression is reduced to A/2, what is the value of the damping coefficient? (Note you will have to solve numerically an implicit equation). 2. Relevant equations x(t) = (A+Bt)e-βt where β = ω0 3. The attempt at a solution A(t) = Ae-βt 1/2A = Ae-βt where t = 1s ln(1/2) = -β I know this can't be right because I'm suppose to arrive at an implicit equation. I can't seem to figure out where I'm going wrong at. Any help would be appreciated.