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| learn:courses:real-analog-chapter-8:start [2017/05/30 20:31] – [Real Analog: Chapter 8] kaitlyn Franz | learn:courses:real-analog-chapter-8:start [2022/10/04 11:38] (current) – external edit 127.0.0.1 | ||
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| ====== 8. Introduction and Chapter Objectives ====== | ====== 8. Introduction and Chapter Objectives ====== | ||
| - | Second order systems are, by definition, systems whose input-output relationship is a //second order// differential equation. A second order differential equation contains a //second order derivative// | + | Second order systems are, by definition, systems whose input-output relationship is a //second order// differential equation. A second order differential equation contains a //second order derivative// |
| Second order systems, like first order systems, are an extremely important class of systems. In previous chapters, we saw that the natural response of first order systems decays exponentially with time – the natural response decays monotonically to zero. The natural response of second order systems can, however, oscillate with time – we will see that a second order systems response can contain sinusoidal components. The motion of a pendulum, for example, can be modeled by a second order system. These oscillations are due to the transfer of energy between the two energy storage mechanisms; a pendulum, for example, oscillates because of the cyclic exchange of potential and kinetic energy of the mass. | Second order systems, like first order systems, are an extremely important class of systems. In previous chapters, we saw that the natural response of first order systems decays exponentially with time – the natural response decays monotonically to zero. The natural response of second order systems can, however, oscillate with time – we will see that a second order systems response can contain sinusoidal components. The motion of a pendulum, for example, can be modeled by a second order system. These oscillations are due to the transfer of energy between the two energy storage mechanisms; a pendulum, for example, oscillates because of the cyclic exchange of potential and kinetic energy of the mass. | ||