Critical damping is a term used to describe a situation where the damping coefficient \(b\) is just great enough that no oscillation occurs. (In critical damping, a moving part is displaced but returns to its equilibrium position quickly without overshooting it.) This is how you want the springs in your car to behave, so that when they flex to take you smoothly over a bump, they don't cause the car to jump up and down, reducing contact with the road.)

(a) For an object of mass \(m\) attached to a spring of spring constant \(k\), what is the value \(b_{\text {crit }}\) needed for critical damping?

(b) Describe the motion if \(b>b_{\text {crit }}\).