Final answer:
Continuous time characteristic equations describe the behavior of continuous time systems, often modeled by differential equations that represent physical phenomena with continuously varying time.
Step-by-step explanation:
Continuous time characteristic equations refer to the equations that describe the behavior of continuous time systems. These systems are typically represented by differential equations that model physical phenomena where time varies continuously, such as oscillations in a spring-mass system or electrical currents in circuits. Differential equations express the relationship between the functions that describe the system's state and their rates of change over time. For instance, instantaneous acceleration in physics, which is a continuous function of time, can be determined from the derivative of the velocity function. This concept is a fundamental part of one-dimensional kinematics and is essential for understanding motion with constant acceleration, as well as more complex systems like two-body pursuit problems. In engineering and physics, simple harmonic motion and electrical circuits involving capacitors and inductors are examples of systems where continuous time characteristic equations are used to predict the future behavior based on initial conditions and constants of the system.