How second order systems respond to sinusoidal/oscillating input. Similar to first order.
For a 2nd order system in standard input-output form:
The gain and phase of the frequency response are therefore:
The plots show gain and phase shift for varying values of
For the electrical system shown below with the values , , find:
- The undamped natural frequency
- The damping factor
- Sketch the magnitude of the frequency response
- At what frequency is this at it's maximum?
- Sketch a bode plot using matlab
The system equation is:
Undamped natural frequency:
Using the graph from the data book
The graph peaks at approx , so:
R = 1000 C = 10e-7 L = 0.1 sys = tf(,[L*C R*C 1]); figure; step(sys); bode(sys);