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Related Concept Videos

Second Order systems II01:18

Second Order systems II

In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
If  ζ...
Types of Damping01:20

Types of Damping

If the amount of damping in a system is gradually increased, the period and frequency start to become affected because damping opposes, and hence slows, the back and forth motion (the net force is smaller in both directions). If there is a very large amount of damping, the system does not even oscillate; instead, it slowly moves toward equilibrium. In brief, an overdamped system moves slowly towards equilibrium, whereas an underdamped system moves quickly to equilibrium but will oscillate about...
Relation between Mathematical Equations and Block Diagrams01:20

Relation between Mathematical Equations and Block Diagrams

In a spring-mass-damper system, the second-order differential equation describes the dynamic behavior of the system. When transformed into the Laplace domain under zero initial conditions, this equation can be effectively analyzed and manipulated. The transformation into the Laplace domain converts differential equations into algebraic equations, simplifying the process of isolating the output.
Types of Responses of Series RLC Circuits01:11

Types of Responses of Series RLC Circuits

A second-order differential equation characterizes a source-free series RLC circuit, marking its distinct mathematical representation. The complete solution of this equation is a blend of two unique solutions, each linked to the circuit's roots expressed in terms of the damping factor and resonant frequency.
Derivatives of Inverse Trigonometric Functions01:30

Derivatives of Inverse Trigonometric Functions

A ship tracking an approaching aircraft relies on geometric measurements to find out the aircraft’s position relative to the observer. By measuring the slant distance to the aircraft and the angle of elevation, the horizontal and vertical components of the distance can be obtained using trigonometric relationships. This geometric approach provides a basis for analyzing how the observed angle changes as the aircraft moves closer to the ship.To examine the mathematical behavior of the angle of...
Damped Oscillations01:07

Damped Oscillations

In the real world, oscillations seldom follow true simple harmonic motion. A system that continues its motion indefinitely without losing its amplitude is termed undamped. However, friction of some sort usually dampens the motion, so it fades away or needs more force to continue. For example, a guitar string stops oscillating a few seconds after being plucked. Similarly, one must continually push a swing to keep a child swinging on a playground.
Although friction and other non-conservative...

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Related Experiment Video

Updated: Jun 3, 2026

Data Acquisition Protocol for Determining Embedded Sensitivity Functions
07:46

Data Acquisition Protocol for Determining Embedded Sensitivity Functions

Published on: April 20, 2016

Understanding dynamics using sensitivity analysis: caveat and solution.

Thanneer M Perumal1, Rudiyanto Gunawan

  • 1Department of Chemical and Biomolecular Engineering, National University of Singapore, Singapore.

BMC Systems Biology
|March 17, 2011
PubMed
Summary
This summary is machine-generated.

Parametric sensitivity analysis (PSA) can mislead understanding of biological model dynamics. A new impulse parametric sensitivity analysis (iPSA) reveals when parameters are important for system behavior, offering more accurate mechanistic insights.

Related Experiment Videos

Last Updated: Jun 3, 2026

Data Acquisition Protocol for Determining Embedded Sensitivity Functions
07:46

Data Acquisition Protocol for Determining Embedded Sensitivity Functions

Published on: April 20, 2016

Area of Science:

  • Computational Systems Biology
  • Biophysics
  • Biochemical Dynamics

Background:

  • Parametric sensitivity analysis (PSA) is widely used in computational systems biology to study parametric dependence in biological models.
  • PSA has been applied to understand cellular processes regulating the dynamics of biological systems.
  • However, PSA coefficients may not be suitable for inferring the mechanisms driving dynamical behavior and can lead to incorrect conclusions.

Purpose of the Study:

  • To explain the limitations of standard Parametric Sensitivity Analysis (PSA) in inferring dynamical mechanisms of biological systems.
  • To introduce a novel sensitivity analysis method, impulse parametric sensitivity analysis (iPSA), to overcome PSA's limitations.
  • To demonstrate the efficacy of iPSA in revealing mechanistic information compared to PSA.

Main Methods:

  • Analysis of parametric perturbations in standard Parametric Sensitivity Analysis (PSA).
  • Development and application of impulse parametric sensitivity analysis (iPSA) using impulse perturbations on system parameters.
  • Illustration of PSA and iPSA efficacy using two examples of switch activation dynamics.

Main Results:

  • PSA coefficients quantify integrated changes from persistent perturbations, losing critical information about when parameter changes affect dynamics.
  • Impulse parametric sensitivity analysis (iPSA) utilizes impulse perturbations to retain temporal information about parameter importance.
  • iPSA demonstrates superior ability to reveal mechanistic insights into dynamical systems compared to PSA.

Conclusions:

  • The persistent nature of perturbations in PSA requires careful interpretation for dynamical systems, as it can be misleading for identifying controlling mechanisms.
  • iPSA, by employing impulse perturbations at different times, provides essential information on how system dynamics are achieved.
  • iPSA clarifies which parameters are essential and the specific times at which they become important for system behavior.