The model of a harmonic oscillator corresponds to a second order system with as the input and as the output. The system is defined by the angular frequency , the attenuation , and the gain .s
Parameters
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Variables
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Attenuation
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Input
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Angular frequency
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Output
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Gain
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The system is defined with the following differential equation
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The transfer function that results from this differential equation can be obtained using the DynamicSystems[TransferFunction] command.
| (2) |
The step response for the corresponding system can be observed by changing the slider values for θ and ω in the following application.
In this example, controls the damping, such that a system with results in a system that is under damped and results in an overshoot. For the cases with the system is over damped and the response has no overshoot. If the system is critically damped, resulting in the fastest rise time of the system without overshooting the final value. The parameter is the natural frequency of the system.
The amplitude is set to 1 for this example.
Step Response Plot Routine
Uncontrolled Step Response
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set value
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set value
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