Final answer:
The rate of change for a damped oscillator's mechanical energy is negative, indicating energy loss over time. It can be represented graphically as a straight line with a negative slope or a curve reflecting an increasing rate of loss.
Step-by-step explanation:
The term that describes the rate of change in the context of a damped oscillator's mechanical energy is key to answering this question. For a damped oscillator, the mechanical energy decreases over time due to the dissipative forces (like friction or air resistance) at work. This means that the time rate of change of mechanical energy for a damped oscillator is negative, reflecting the ongoing energy loss.
Looking at the options provided and considering the nature of a damped oscillator, we see that the correct answer is:
b. Negative
This negative rate of change might be represented graphically as a straight line with a negative slope, indicating a constant rate of energy decrease, or as a curve that shows an increasing rate of negative values over time if the rate of energy dissipation increases.