OpenStax College Physics for AP® Courses, Chapter 16, Problem 16 (Test Prep for AP® Courses)

This is College Physics Answers with Shaun Dychko. This question is asking for the time rate of change of mechanical energy for a damped oscillator so this is using fancy words to say something that's not so complicated. Let's first think about what a damped oscillator is. So it's an oscillator where there's friction that's dissipating some of the kinetic energy of the oscillator— the kinetic energy is a type of mechanical energy. So some of the mechanical energy is turning into heat or sound and so it's losing mechanical energy because of this damping force, which is usually friction. So when loosing mechanical energy that means the rate of change of mechanical energy is negative because a negative rate of change represents a loss in something and so the answer is (b).