How do I identify a dynamic or static system?

To determine if a system is static or dynamic, you analyze its behavior over time and how it responds to changes in input. Here's a guide: Static System: A system is static if its output depends only on the current input and not on past or future inputs. These systems have no memory or time-dependent behavior. Key Characteristics: 1. Output is an immediate function of the current input. 2. No storage or feedback of past inputs. 3. Typically represented algebraically (e.g., ). Examples: A resistor in an electrical circuit (). A spring under static load (Hooke’s Law: ). Basic arithmetic operations (e.g., ). Test for Static Behavior: Change the input and observe the output. If the output changes instantaneously and is unaffected by prior inputs, the system is static. Dynamic System: A system is dynamic if its output depends on the current input and past inputs (or their rates of change). These systems have memory or storage elements that make the output time-dependent. Key Characteristics: 1. Output depends on the system's history or state. 2. Time plays a significant role (e.g., differential or difference equations describe them). 3. Can involve feedback loops, energy storage, or delays. Examples: A capacitor or inductor in an electrical circuit (governed by differential equations). A pendulum (output depends on motion history). Population growth models. Systems with integration or differentiation ( or ). Test for Dynamic Behavior: Apply an input change and observe the output. If the output changes gradually, depends on the rate of input change, or persists after the input is removed, the system is dynamic. Key Indicators to Differentiate: Practical Example: 1. Thermometer: If it reads the temperature instantly based on current conditions, it’s static. If it takes time to reach the reading (e.g., due to thermal lag), it’s dynamic. 2. Car Suspension: Responds to road bumps based on both the current and previous positions of the car. This makes it dynamic.

Static systems usually are "simple": they respond almost instantaneously to an input, no "thinking" necessary, as their answer depends only on that input. (Example: a resistance - current changes instantly with voltage change) If a system needs to consider not just the last input but previous ones as well, then it will take a bit more time to react/provide an answer: it should be a dynamic system. (Example: charge-coupled device (CCD) sensors - the "eyes" in some devices to capture light from astronomy, for instance): accumulates and transfers charge based on incident light over time. So, these two aspects, response time and which inputs are effectively used should determine, with a good level of precision , whether a system is static or dynamic. Of course, some dynamic system can have quick enough responses to be categorized as static.

Dynamic System Definition: A system whose output changes over time in response to its inputs or initial conditions. 1) The state of the system evolves over time. 2) It depends on past inputs or states (e.g., feedback loops). Examples: A moving pendulum. Static System Definition: A system whose output depends only on the current input without considering past or future states. Key Features: 1) The output is instantaneous and doesn't change unless the input changes. 2) It does not depend on past inputs or states. Examples: A scale measuring weight.

Static systems in engineering don't move, don't change states, or don't change states rapidly. Static systems include things like buildings, bridges, furniture, and dishes. By definition, dynamic systems are always changing states or moving, or they need to change states in order to be useful.

Static does not change with time. We could say that dynamic is the opposite for simplicity.

Mathematically, A dynamic system is described by a differential equation (or difference equation) while a static system is described by an algebraic equation.