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learn:courses:real-analog-chapter-8:start [2017/05/30 18:28] – [Real Analog: Chapter 8] Marthalearn:courses:real-analog-chapter-8:start [2022/10/04 11:38] (current) – external edit 127.0.0.1
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 ====== Real Analog: Chapter 8 ====== ====== Real Analog: Chapter 8 ======
 [[{}/learn/courses/real-analog-chapter-7/start|Back to Chapter 7]] [[{}/learn/courses/real-analog-chapter-7/start|Back to Chapter 7]]
--->Chapter 8 Downloads#   +-->Chapter 8 Materials#   
-  * Lecture Slides:+  * Lecture Material:
     * {{ :learn:courses:real-analog-chapter-8:lecture20_b_.ppt |Lecture 20(b) PowerPoint Slides}}: First-order circuit step response, introduction to second-order systems     * {{ :learn:courses:real-analog-chapter-8:lecture20_b_.ppt |Lecture 20(b) PowerPoint Slides}}: First-order circuit step response, introduction to second-order systems
     * {{ :learn:courses:real-analog-chapter-8:lecture21.ppt |Lecture 21 PowerPoint Slides}}: Second-order circuit natural response, sinusoidal signals & complex exponentials     * {{ :learn:courses:real-analog-chapter-8:lecture21.ppt |Lecture 21 PowerPoint Slides}}: Second-order circuit natural response, sinusoidal signals & complex exponentials
     * {{ :learn:courses:real-analog-chapter-8:lecture22.ppt |Lecture 22 PowerPoint Slides}}: Second-order system natural response, mathematical form of solutions, qualitative interpretation     * {{ :learn:courses:real-analog-chapter-8:lecture22.ppt |Lecture 22 PowerPoint Slides}}: Second-order system natural response, mathematical form of solutions, qualitative interpretation
     * {{ :learn:courses:real-analog-chapter-8:lecture23.ppt |Lecture 23 PowerPoint Slides}}: Second-order system step response, governing equation, mathematical expression, estimating step response, examples     * {{ :learn:courses:real-analog-chapter-8:lecture23.ppt |Lecture 23 PowerPoint Slides}}: Second-order system step response, governing equation, mathematical expression, estimating step response, examples
 +    * [[http://www.youtube.com/watch?v=iDZOK86gjMI&list=PLDEC730F6A8CDE318&index=23&feature=plpp_video| Lecture 20(b) Video]]
 +    * [[http://www.youtube.com/watch?v=lOaav2j-ZjM&list=PLDEC730F6A8CDE318&index=24&feature=plpp_video| Lecture 21 Video]]
 +    * [[http://www.youtube.com/watch?v=lcjf9lQXjSw&list=PLDEC730F6A8CDE318&index=25&feature=plpp_video| Lecture 22 Video]]
 +    * [[http://www.youtube.com/watch?v=uUP4J7dyF8o&list=PLDEC730F6A8CDE318&index=26&feature=plpp_video| Lecture 23 Video]]
 +  * Chapter 8 Video:
 +    * [[http://www.youtube.com/watch?v=TIeKihNmNZM&list=PL170A01159D42313D&index=18&feature=plpp_video| Lab 8 Video 1]]: Second Order Circuit Step Response: Measuring the step response of a series RLC circuit. The measured peak value of the response is compared to analytical expectations.
   * {{ :learn:courses:real-analog-chapter-8:real-analog-chapter-8.pdf | Chapter 8 Complete PDF}}   * {{ :learn:courses:real-analog-chapter-8:real-analog-chapter-8.pdf | Chapter 8 Complete PDF}}
     * {{ :learn:courses:real-analog-chapter-8:lab8p5p1.pdf |Lab 8.5.1}}     * {{ :learn:courses:real-analog-chapter-8:lab8p5p1.pdf |Lab 8.5.1}}
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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// but no derivative higher than second order. Second order systems contain //two independent energy storage elements//, per our comments in [[https://reference.digilentinc.com/learn/courses/real-analog-chapter-7/start|Chapter 7]] pertaining to the relationship between the number of energy storage elements in a system and the system order+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// but no derivative higher than second order. Second order systems contain //two independent energy storage elements//, per our comments in [[/learn/courses/real-analog-chapter-7/start|Chapter 7]] pertaining to the relationship between the number of energy storage elements in a system and the system order
  
 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.