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In control theory, the main difference between first order and second order systems lies in their response to input signals.

First order systems have a single energy storage element, such as a capacitor or inductor, and their response to input signals is characterized by a first-order differential equation. These systems have a slower response time and exhibit a single exponential decay or growth in their output.

On the other hand, second order systems have two energy storage elements and their response is governed by a second-order differential equation. These systems have a faster response time compared to first order systems and can exhibit oscillatory behavior in their output response.

In summary, the key distinction between first order and second order systems in control theory is their complexity and response characteristics, with second order systems generally having a faster and more dynamic response compared to first order systems.

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