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This document discusses the response of linear single degree of freedom (SDOF) systems to general loading through the use of superposition. It introduces the mass-spring-damper model and defines two special free response functions: the unit amplitude free decay function and the unit velocity free decay function. It explains that the general solution to the forced response of a SDOF system can be constructed by taking a superposition of responses to these two base functions using the initial conditions and applied force over time.

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Response spectrum

This document discusses different types of structural response spectra used to analyze how structures respond to dynamic loads like earthquakes. It defines static load response, dynamic load response, and equations of motion. It explains D'Alembert's principle of dynamic equilibrium and how response depends on natural frequency and damping ratio. It then describes response time histories obtained from accelerographs and how response spectra are developed based on maximum deformation of single-degree-of-freedom systems subjected to ground motions. Finally, it defines pseudo-velocity, pseudo-acceleration response spectra and how each spectrum provides a meaningful physical quantity - deformation, strain energy, or equivalent static force.

Structural Dynamics - SDOF

1) The document introduces single-degree-of-freedom (SDOF) structural dynamics systems. SDOF systems have a single mass that translates or rotates in one direction.
2) Basic concepts are discussed including degrees of freedom, Newton's second law, and the equation of motion for an SDOF system with an external force or base excitation.
3) Solutions to the equation of motion are explored for undamped free vibration and undamped forced vibration cases. The solution for undamped free vibration takes the form of simple harmonic motion.

DOMV No 3 RESPONSE OF LINEAR SDOF SYSTEMS TO GENERAL LOADING (1).pdf

There are two unique functions needed to generate the general response of a single-degree-of-freedom (SDOF) system to arbitrary forcing: the unit amplitude free decay function and the unit velocity free decay function. The impulse response function is identical to the unit velocity free decay function. The lecture will consider four scenarios involving the impulse response function to build up the solution to general forcing. This will demonstrate that only the impulse response function is needed to determine the response of an SDOF system to any input, from any initial conditions.

Meeting w4 chapter 2 part 2

The document discusses modeling of electrical and mechanical systems. It provides examples of modeling an RLC network, DC motor, spring-mass-damper system, and closed-loop position control system using transfer functions derived from equations of motion. Transfer functions are obtained using Laplace transforms of differential equations describing the dynamics of the systems.

Meeting w4 chapter 2 part 2

The document discusses modeling of electrical and mechanical systems. It provides examples of modeling translational and rotational mechanical systems including springs, masses, dampers, motors, and gears. It derives transfer functions for various systems using equations of motion and Laplace transforms. One example shows modeling a closed-loop position control system with a motor, gears, load, and position feedback.

Proje kt

We present a class of continuous, bounded, finite-time stabilizing controllers for the tranlational and double integrator based on Bhat and Bernstein's work of IEEE Transactions on Automatic Control, Vol. 43, No. 5, May 1998

Oscillations

This document discusses oscillations and wave motion. It begins by introducing mechanical vibrations and simple harmonic motion. It then covers damped and driven oscillations, as well as different oscillating systems like springs, pendulums, and driven oscillations. The document goes on to discuss traveling waves, the wave equation, periodic waves on strings and in electromagnetic fields. It also covers waves in three dimensions, reflection, refraction, diffraction, and interference of waves. Key concepts covered include amplitude, frequency, period, angular frequency, energy of oscillating systems, and resonance.

Lecture1 NPTEL for Basics of Vibrations for Simple Mechanical Systems

This document provides an introduction to vibrations and oscillations in mechanical systems. It discusses linear systems and how they relate an input signal to an output signal. As an example, it describes how forces acting on a vehicle excite vibrations that produce sound pressures in the passenger compartment. It then focuses on modeling single degree of freedom spring-mass and spring-mass-damper systems, providing the equations of motion for each and discussing how to determine the system parameters like stiffness from experiments. The key goals are to understand vibrations in simple mechanical systems using linear differential equations.

Response spectrum

This document discusses different types of structural response spectra used to analyze how structures respond to dynamic loads like earthquakes. It defines static load response, dynamic load response, and equations of motion. It explains D'Alembert's principle of dynamic equilibrium and how response depends on natural frequency and damping ratio. It then describes response time histories obtained from accelerographs and how response spectra are developed based on maximum deformation of single-degree-of-freedom systems subjected to ground motions. Finally, it defines pseudo-velocity, pseudo-acceleration response spectra and how each spectrum provides a meaningful physical quantity - deformation, strain energy, or equivalent static force.

Structural Dynamics - SDOF

1) The document introduces single-degree-of-freedom (SDOF) structural dynamics systems. SDOF systems have a single mass that translates or rotates in one direction.
2) Basic concepts are discussed including degrees of freedom, Newton's second law, and the equation of motion for an SDOF system with an external force or base excitation.
3) Solutions to the equation of motion are explored for undamped free vibration and undamped forced vibration cases. The solution for undamped free vibration takes the form of simple harmonic motion.

DOMV No 3 RESPONSE OF LINEAR SDOF SYSTEMS TO GENERAL LOADING (1).pdf

There are two unique functions needed to generate the general response of a single-degree-of-freedom (SDOF) system to arbitrary forcing: the unit amplitude free decay function and the unit velocity free decay function. The impulse response function is identical to the unit velocity free decay function. The lecture will consider four scenarios involving the impulse response function to build up the solution to general forcing. This will demonstrate that only the impulse response function is needed to determine the response of an SDOF system to any input, from any initial conditions.

Meeting w4 chapter 2 part 2

The document discusses modeling of electrical and mechanical systems. It provides examples of modeling an RLC network, DC motor, spring-mass-damper system, and closed-loop position control system using transfer functions derived from equations of motion. Transfer functions are obtained using Laplace transforms of differential equations describing the dynamics of the systems.

Meeting w4 chapter 2 part 2

The document discusses modeling of electrical and mechanical systems. It provides examples of modeling translational and rotational mechanical systems including springs, masses, dampers, motors, and gears. It derives transfer functions for various systems using equations of motion and Laplace transforms. One example shows modeling a closed-loop position control system with a motor, gears, load, and position feedback.

Proje kt

We present a class of continuous, bounded, finite-time stabilizing controllers for the tranlational and double integrator based on Bhat and Bernstein's work of IEEE Transactions on Automatic Control, Vol. 43, No. 5, May 1998

Oscillations

This document discusses oscillations and wave motion. It begins by introducing mechanical vibrations and simple harmonic motion. It then covers damped and driven oscillations, as well as different oscillating systems like springs, pendulums, and driven oscillations. The document goes on to discuss traveling waves, the wave equation, periodic waves on strings and in electromagnetic fields. It also covers waves in three dimensions, reflection, refraction, diffraction, and interference of waves. Key concepts covered include amplitude, frequency, period, angular frequency, energy of oscillating systems, and resonance.

Lecture1 NPTEL for Basics of Vibrations for Simple Mechanical Systems

This document provides an introduction to vibrations and oscillations in mechanical systems. It discusses linear systems and how they relate an input signal to an output signal. As an example, it describes how forces acting on a vehicle excite vibrations that produce sound pressures in the passenger compartment. It then focuses on modeling single degree of freedom spring-mass and spring-mass-damper systems, providing the equations of motion for each and discussing how to determine the system parameters like stiffness from experiments. The key goals are to understand vibrations in simple mechanical systems using linear differential equations.

IC8451 Control Systems

This document contains a question bank for control systems with questions about various control system concepts. Some key points:
1. It defines open loop and closed loop control systems, with closed loop systems having feedback to correct errors and maintain desired output values.
2. The components of a feedback control system are identified as the plant, feedback path, error detector, actuator and controller.
3. Different types of controllers are listed, including proportional, PI, PD and PID controllers. The proportional controller produces an output proportional to the error signal.

Transfer fn mech. systm

The document defines transfer function as the ratio of the Laplace transform of the output to the input of a system with zero initial conditions. It discusses poles and zeros, which are values of s that make the transfer function tend to infinity or zero. Strictly proper, proper, and improper transfer functions are classified based on the order of the numerator and denominator polynomials. The characteristic equation is obtained by equating the denominator of the transfer function to zero. Advantages of transfer functions include representing systems with algebraic equations and determining poles, zeros and differential equations. Translational and rotational mechanical systems are described along with their resisting forces, and D'Alembert's principle is explained.

Projekt

The document proposes continuous finite-time stabilizing controllers for the translational and rotational double integrator systems. It begins by introducing the problem and motivation for developing continuous finite-time controllers. It then presents a controller for the translational double integrator that renders the origin globally finite-time stable. The controller is modified to produce bounded feedback and avoid issues like unwinding. Finally, the controller is adapted for the rotational double integrator to stabilize angular position while avoiding unwinding through periodicity in the feedback law.

Time response analysis of system

Time Response Analysis of system
Standard Test Signals
What is time response ?
Types of Responses
Analysis of First order system
Analysis of Second order system

Me330 lecture5

This document discusses modeling mechanical systems for control systems. It covers:
1) Newton's second law governs mechanical systems and results in equations of motion describing dynamical systems. These equations can be represented using block diagrams and Laplace transforms.
2) Modeling involves determining the equation of motion using free body diagrams and summing the forces. Mechanical components like springs, dampers and masses have characteristic force-velocity, force-displacement and impedance relationships.
3) Systems with multiple degrees of freedom require equations of motion equal to the number of independent motions. Transfer functions can be derived from the Laplace transform of the equations of motion.

Ordinary Differential Equations And Their Application: Modeling: Free Oscilla...

1) The document discusses ordinary differential equations that model free oscillations of a spring-mass system and electric circuits.
2) It derives the differential equation for simple harmonic motion of a mass attached to a spring as well as cases with damping.
3) Kirchhoff's voltage law is used to derive differential equations for simple R-L and R-C circuits driven by external voltages.
4) As an example, the differential equation for a series R-C circuit is solved analytically to find expressions for charge and current over time.

impulse(GreensFn), Principle of Superposition

Impulse superposition
Green’s function for underdamped oscillator
Exponential driving force
Green’s function for an undamped oscillator
Solution for constant force
Step function method

lecture1 (5).ppt

This document discusses transient and steady state response analysis of first and second order systems. It begins by defining transient response as the system response from the initial to final state, and steady state response as the system output behavior as time approaches infinity after the transient response decays. For first order systems, it derives the step response and defines the time constant. For second order systems, it discusses the different response types based on the damping ratio and derives expressions for transient response specifications like rise time, peak time, and settling time in terms of the damping ratio and natural frequency.

3- Mechanical Vibration.pptx

This document discusses the response of 1-degree-of-freedom systems to harmonic excitation. It covers:
1) The response of an undamped system, which has a steady state solution that is the sum of the homogeneous and particular solutions. The maximum amplitude is proportional to the force amplitude divided by the spring stiffness.
2) The response of a damped system, where the maximum amplitude depends on the frequency ratio and damping ratio. It is highest at resonance when the forcing frequency matches the natural frequency.
3) Applications to damped systems subjected to harmonic base motion, rotating unbalance, or other periodic excitations. The ratio of response amplitude to static deflection is called the magnification or amplification factor

z transforms

This document discusses signals and systems. It defines signals as physical quantities that vary with respect to time, space, or another independent variable. Signals can be classified as discrete time or continuous time. It also defines unit impulse and unit step functions for discrete and continuous time. Periodic and aperiodic signals are discussed. The Fourier series and Fourier transform are introduced as ways to represent signals in the frequency domain. The Laplace transform, which generalizes the Fourier transform, is also mentioned. Key properties of linear time-invariant systems like superposition, time-invariance, and convolution are covered. Finally, sampling theory and the z-transform, which is analogous to the Laplace transform for discrete-time systems, are summarized at a high level

5. fourier properties

The document summarizes properties and examples of the Fourier transform. It discusses:
1) The Fourier transform represents the frequency content of a signal and relates a signal x(t) to its frequency domain representation X(jω).
2) The Fourier transform is a linear operator, so transforms of summed signals are the sums of the individual transforms. Additionally, a time shift in the signal results in a phase shift in the frequency domain representation.
3) Differentiation in the time domain corresponds to multiplication by jω in the frequency domain. Convolution in the time domain is represented by simple multiplication of the frequency domain representations. This allows solving differential equations using Fourier transforms.

signals and system

1) A signal is a physical quantity that varies with respect to time, space, or other independent variables. Signals can be classified as discrete or continuous. 2) Unit impulse and unit step signals are defined for both discrete and continuous time. The discrete unit impulse is 1 at n=0 and 0 otherwise. The continuous unit impulse is 1 at t=0 and 0 otherwise. 3) Periodic signals repeat over a time period T, while aperiodic signals do not have this periodicity property. Even and odd signals satisfy certain symmetry properties when their argument is negated.

Physics formulas list

The document provides a list of physics formulas across various topics in mechanics, electricity, thermodynamics, and more. It begins with an introduction on studying physics and understanding concepts through visualization of problems. The bulk of the document then lists key formulas in different areas of physics, providing the formulas and brief explanations. It encourages readers to derive the formulas themselves and find the joy in solving problems independently.

lec02.pdf

The document outlines the plan for a lecture on state-space models of systems and linearization. It will begin with a review of control and feedback concepts. The main topic will be introducing state-space models, which provide a general framework for representing different types of systems with differential equations. Examples will be used to illustrate how to derive state-space models from physical systems like masses on springs, electrical circuits, and pendulums. The goal is for students to master the state-space modeling approach in order to enable later analysis and design of systems.

dampedvibration02-160513044006.pdf

Damped vibration refers to vibration with decreasing amplitude over time due to frictional forces. The differential equation that describes damped harmonic vibration contains damping coefficients that represent internal or external forces. There are three types of solutions to the equation of motion for a damped single degree of freedom system - critically damped, overdamped, and underdamped. When a damped oscillator is subjected to an external harmonic forcing function, the response consists of an initial transient response that decays and a steady-state response whose amplitude and phase depend on the forcing frequency relative to the natural frequency.

lecture3_2.pdf

1) The lecture discusses the time domain analysis of continuous time linear and time-invariant systems. It covers topics such as impulse response, convolution, and how the output of an LTI system can be determined from its impulse response and the input signal.
2) An example of analyzing the voltage response of an RC circuit to an arbitrary input is presented. The output is the sum of the zero-input response, due to initial conditions, and zero-state response, which is a convolution of the impulse response and input signal.
3) Detectors of high energy photons can be modeled as having an exponential decay impulse response. Examples of characterizing real detectors through measurements of energy resolution, timing resolution, and coincidence point spread

Unit v rpq1

The document defines and discusses properties of linear systems with random inputs. It can be summarized as follows:
1) A linear system is one where the output is a linear combination of the input. The properties of linear systems include that the input and output are related by a convolution integral and the power spectral densities of the input and output are related by the system transfer function.
2) If the input to a linear, time-invariant system is a wide-sense stationary (WSS) process, the output will also be WSS.
3) The unit impulse response of a system is its output when the input is a unit impulse. It is also called the system weighting function if the output is defined as

dicover the new book of halloween

The document provides an overview of vibration dynamics and modeling. It discusses:
1) Vibrations are oscillations about an equilibrium position, which can be desirable or undesirable depending on the application.
2) Analyzing the dynamics of vibrating systems is important for all vibration control approaches, including passive, semi-active, and active controls.
3) Mathematical models of vibrations are introduced, starting with the simple case of free vibration of an undamped single-degree-of-freedom system and gradually increasing the complexity by adding damping and multiple degrees of freedom.

Basic vibration dynamics

The document provides an overview of vibration dynamics and modeling. It discusses:
1) Vibrations are oscillations about an equilibrium position, which can be desirable or undesirable depending on the application.
2) Analyzing the dynamics of vibrating systems is important for all vibration control approaches, including passive, semi-active, and active controls.
3) Mathematical models of vibrations are introduced, starting with the simple single degree of freedom mass-spring-damper system and building in complexity to multi-degree of freedom systems and continuous structures.

time response analysis

This document provides an analysis of the time response of control systems. It defines time response as the output of a system over time in response to an input that varies over time. The time response analysis is divided into transient response, which decays over time, and steady state response. Different types of input signals are described, including step, ramp, and sinusoidal inputs. Methods for analyzing the first and second order systems are presented, including determining the transient and steady state response. Static error coefficients like position, velocity and acceleration constants are defined for different system types and inputs. Examples are provided to illustrate the analysis of first and second order systems.

Sensors_2020.pptx

This document discusses various types of robotic sensors. It begins by explaining why robots need sensors to provide awareness of their surroundings, allow interaction with the environment, and enable goal-seeking behaviors. The document then describes different things that can be sensed by robotic sensors, such as light, sound, heat, chemicals, and object proximity. Several common types of robotic sensors are outlined, including feelers, photoelectric, infrared, ultrasonic, visual, and chemical sensors. The characteristics and functions of proximity, inductive, capacitive, and optical proximity sensors are explained in more detail. The document aims to provide an overview of the role and functionality of different robotic sensors.

DOMV No 12 CONTINUED ADVANCED KINEMATIC ANALYSIS v2.pdf

The document discusses the derivation of position, velocity, and acceleration vectors for a particle moving in a plane when described using a rotating reference frame. It shows that the position vector in the rotating frame is simply the particle's radius vector. The velocity vector has components of radial velocity and tangential velocity due to rotation. Similarly, the acceleration vector has radial and tangential acceleration components as well as a centrifugal acceleration term. These relationships are obtained through rotation of axes transformations.

IC8451 Control Systems

This document contains a question bank for control systems with questions about various control system concepts. Some key points:
1. It defines open loop and closed loop control systems, with closed loop systems having feedback to correct errors and maintain desired output values.
2. The components of a feedback control system are identified as the plant, feedback path, error detector, actuator and controller.
3. Different types of controllers are listed, including proportional, PI, PD and PID controllers. The proportional controller produces an output proportional to the error signal.

Transfer fn mech. systm

The document defines transfer function as the ratio of the Laplace transform of the output to the input of a system with zero initial conditions. It discusses poles and zeros, which are values of s that make the transfer function tend to infinity or zero. Strictly proper, proper, and improper transfer functions are classified based on the order of the numerator and denominator polynomials. The characteristic equation is obtained by equating the denominator of the transfer function to zero. Advantages of transfer functions include representing systems with algebraic equations and determining poles, zeros and differential equations. Translational and rotational mechanical systems are described along with their resisting forces, and D'Alembert's principle is explained.

Projekt

The document proposes continuous finite-time stabilizing controllers for the translational and rotational double integrator systems. It begins by introducing the problem and motivation for developing continuous finite-time controllers. It then presents a controller for the translational double integrator that renders the origin globally finite-time stable. The controller is modified to produce bounded feedback and avoid issues like unwinding. Finally, the controller is adapted for the rotational double integrator to stabilize angular position while avoiding unwinding through periodicity in the feedback law.

Time response analysis of system

Time Response Analysis of system
Standard Test Signals
What is time response ?
Types of Responses
Analysis of First order system
Analysis of Second order system

Me330 lecture5

This document discusses modeling mechanical systems for control systems. It covers:
1) Newton's second law governs mechanical systems and results in equations of motion describing dynamical systems. These equations can be represented using block diagrams and Laplace transforms.
2) Modeling involves determining the equation of motion using free body diagrams and summing the forces. Mechanical components like springs, dampers and masses have characteristic force-velocity, force-displacement and impedance relationships.
3) Systems with multiple degrees of freedom require equations of motion equal to the number of independent motions. Transfer functions can be derived from the Laplace transform of the equations of motion.

Ordinary Differential Equations And Their Application: Modeling: Free Oscilla...

1) The document discusses ordinary differential equations that model free oscillations of a spring-mass system and electric circuits.
2) It derives the differential equation for simple harmonic motion of a mass attached to a spring as well as cases with damping.
3) Kirchhoff's voltage law is used to derive differential equations for simple R-L and R-C circuits driven by external voltages.
4) As an example, the differential equation for a series R-C circuit is solved analytically to find expressions for charge and current over time.

impulse(GreensFn), Principle of Superposition

Impulse superposition
Green’s function for underdamped oscillator
Exponential driving force
Green’s function for an undamped oscillator
Solution for constant force
Step function method

lecture1 (5).ppt

This document discusses transient and steady state response analysis of first and second order systems. It begins by defining transient response as the system response from the initial to final state, and steady state response as the system output behavior as time approaches infinity after the transient response decays. For first order systems, it derives the step response and defines the time constant. For second order systems, it discusses the different response types based on the damping ratio and derives expressions for transient response specifications like rise time, peak time, and settling time in terms of the damping ratio and natural frequency.

3- Mechanical Vibration.pptx

This document discusses the response of 1-degree-of-freedom systems to harmonic excitation. It covers:
1) The response of an undamped system, which has a steady state solution that is the sum of the homogeneous and particular solutions. The maximum amplitude is proportional to the force amplitude divided by the spring stiffness.
2) The response of a damped system, where the maximum amplitude depends on the frequency ratio and damping ratio. It is highest at resonance when the forcing frequency matches the natural frequency.
3) Applications to damped systems subjected to harmonic base motion, rotating unbalance, or other periodic excitations. The ratio of response amplitude to static deflection is called the magnification or amplification factor

z transforms

This document discusses signals and systems. It defines signals as physical quantities that vary with respect to time, space, or another independent variable. Signals can be classified as discrete time or continuous time. It also defines unit impulse and unit step functions for discrete and continuous time. Periodic and aperiodic signals are discussed. The Fourier series and Fourier transform are introduced as ways to represent signals in the frequency domain. The Laplace transform, which generalizes the Fourier transform, is also mentioned. Key properties of linear time-invariant systems like superposition, time-invariance, and convolution are covered. Finally, sampling theory and the z-transform, which is analogous to the Laplace transform for discrete-time systems, are summarized at a high level

5. fourier properties

The document summarizes properties and examples of the Fourier transform. It discusses:
1) The Fourier transform represents the frequency content of a signal and relates a signal x(t) to its frequency domain representation X(jω).
2) The Fourier transform is a linear operator, so transforms of summed signals are the sums of the individual transforms. Additionally, a time shift in the signal results in a phase shift in the frequency domain representation.
3) Differentiation in the time domain corresponds to multiplication by jω in the frequency domain. Convolution in the time domain is represented by simple multiplication of the frequency domain representations. This allows solving differential equations using Fourier transforms.

signals and system

1) A signal is a physical quantity that varies with respect to time, space, or other independent variables. Signals can be classified as discrete or continuous. 2) Unit impulse and unit step signals are defined for both discrete and continuous time. The discrete unit impulse is 1 at n=0 and 0 otherwise. The continuous unit impulse is 1 at t=0 and 0 otherwise. 3) Periodic signals repeat over a time period T, while aperiodic signals do not have this periodicity property. Even and odd signals satisfy certain symmetry properties when their argument is negated.

Physics formulas list

The document provides a list of physics formulas across various topics in mechanics, electricity, thermodynamics, and more. It begins with an introduction on studying physics and understanding concepts through visualization of problems. The bulk of the document then lists key formulas in different areas of physics, providing the formulas and brief explanations. It encourages readers to derive the formulas themselves and find the joy in solving problems independently.

lec02.pdf

The document outlines the plan for a lecture on state-space models of systems and linearization. It will begin with a review of control and feedback concepts. The main topic will be introducing state-space models, which provide a general framework for representing different types of systems with differential equations. Examples will be used to illustrate how to derive state-space models from physical systems like masses on springs, electrical circuits, and pendulums. The goal is for students to master the state-space modeling approach in order to enable later analysis and design of systems.

dampedvibration02-160513044006.pdf

Damped vibration refers to vibration with decreasing amplitude over time due to frictional forces. The differential equation that describes damped harmonic vibration contains damping coefficients that represent internal or external forces. There are three types of solutions to the equation of motion for a damped single degree of freedom system - critically damped, overdamped, and underdamped. When a damped oscillator is subjected to an external harmonic forcing function, the response consists of an initial transient response that decays and a steady-state response whose amplitude and phase depend on the forcing frequency relative to the natural frequency.

lecture3_2.pdf

1) The lecture discusses the time domain analysis of continuous time linear and time-invariant systems. It covers topics such as impulse response, convolution, and how the output of an LTI system can be determined from its impulse response and the input signal.
2) An example of analyzing the voltage response of an RC circuit to an arbitrary input is presented. The output is the sum of the zero-input response, due to initial conditions, and zero-state response, which is a convolution of the impulse response and input signal.
3) Detectors of high energy photons can be modeled as having an exponential decay impulse response. Examples of characterizing real detectors through measurements of energy resolution, timing resolution, and coincidence point spread

Unit v rpq1

The document defines and discusses properties of linear systems with random inputs. It can be summarized as follows:
1) A linear system is one where the output is a linear combination of the input. The properties of linear systems include that the input and output are related by a convolution integral and the power spectral densities of the input and output are related by the system transfer function.
2) If the input to a linear, time-invariant system is a wide-sense stationary (WSS) process, the output will also be WSS.
3) The unit impulse response of a system is its output when the input is a unit impulse. It is also called the system weighting function if the output is defined as

dicover the new book of halloween

The document provides an overview of vibration dynamics and modeling. It discusses:
1) Vibrations are oscillations about an equilibrium position, which can be desirable or undesirable depending on the application.
2) Analyzing the dynamics of vibrating systems is important for all vibration control approaches, including passive, semi-active, and active controls.
3) Mathematical models of vibrations are introduced, starting with the simple case of free vibration of an undamped single-degree-of-freedom system and gradually increasing the complexity by adding damping and multiple degrees of freedom.

Basic vibration dynamics

The document provides an overview of vibration dynamics and modeling. It discusses:
1) Vibrations are oscillations about an equilibrium position, which can be desirable or undesirable depending on the application.
2) Analyzing the dynamics of vibrating systems is important for all vibration control approaches, including passive, semi-active, and active controls.
3) Mathematical models of vibrations are introduced, starting with the simple single degree of freedom mass-spring-damper system and building in complexity to multi-degree of freedom systems and continuous structures.

time response analysis

This document provides an analysis of the time response of control systems. It defines time response as the output of a system over time in response to an input that varies over time. The time response analysis is divided into transient response, which decays over time, and steady state response. Different types of input signals are described, including step, ramp, and sinusoidal inputs. Methods for analyzing the first and second order systems are presented, including determining the transient and steady state response. Static error coefficients like position, velocity and acceleration constants are defined for different system types and inputs. Examples are provided to illustrate the analysis of first and second order systems.

IC8451 Control Systems

IC8451 Control Systems

Transfer fn mech. systm

Transfer fn mech. systm

Projekt

Projekt

Time response analysis of system

Time response analysis of system

Me330 lecture5

Me330 lecture5

Ordinary Differential Equations And Their Application: Modeling: Free Oscilla...

Ordinary Differential Equations And Their Application: Modeling: Free Oscilla...

impulse(GreensFn), Principle of Superposition

impulse(GreensFn), Principle of Superposition

lecture1 (5).ppt

lecture1 (5).ppt

3- Mechanical Vibration.pptx

3- Mechanical Vibration.pptx

z transforms

z transforms

5. fourier properties

5. fourier properties

signals and system

signals and system

Physics formulas list

Physics formulas list

lec02.pdf

lec02.pdf

dampedvibration02-160513044006.pdf

dampedvibration02-160513044006.pdf

lecture3_2.pdf

lecture3_2.pdf

Unit v rpq1

Unit v rpq1

dicover the new book of halloween

dicover the new book of halloween

Basic vibration dynamics

Basic vibration dynamics

time response analysis

time response analysis

Sensors_2020.pptx

This document discusses various types of robotic sensors. It begins by explaining why robots need sensors to provide awareness of their surroundings, allow interaction with the environment, and enable goal-seeking behaviors. The document then describes different things that can be sensed by robotic sensors, such as light, sound, heat, chemicals, and object proximity. Several common types of robotic sensors are outlined, including feelers, photoelectric, infrared, ultrasonic, visual, and chemical sensors. The characteristics and functions of proximity, inductive, capacitive, and optical proximity sensors are explained in more detail. The document aims to provide an overview of the role and functionality of different robotic sensors.

DOMV No 12 CONTINUED ADVANCED KINEMATIC ANALYSIS v2.pdf

The document discusses the derivation of position, velocity, and acceleration vectors for a particle moving in a plane when described using a rotating reference frame. It shows that the position vector in the rotating frame is simply the particle's radius vector. The velocity vector has components of radial velocity and tangential velocity due to rotation. Similarly, the acceleration vector has radial and tangential acceleration components as well as a centrifugal acceleration term. These relationships are obtained through rotation of axes transformations.

DOMV No 5 MATH MODELLING Newtonian d'Alembert Virtual Work (1).pdf

This document discusses different approaches for constructing mathematical models from physical systems:
1) Newtonian mechanics uses Newton's second law to directly obtain equations of motion for lumped mass systems.
2) D'Alembert's principle allows inertia forces to be included in equilibrium diagrams, making it useful for continuous systems.
3) The principle of virtual work equates the total virtual work done by internal and external forces during virtual displacements to zero, providing another approach for developing equations of motion. Examples are provided to illustrate Newtonian mechanics and the principle of virtual work.

DOMV No 8 MDOF LINEAR SYSTEMS - RAYLEIGH'S METHOD - FREE VIBRATION.pdf

This document discusses free vibration analysis of linear multi-degree-of-freedom (MDOF) systems. It introduces Rayleigh's method, an approximate technique to determine natural frequencies of MDOF systems by assuming harmonic motion. Rayleigh's method equates maximum kinetic energy to maximum potential energy to derive an expression for natural frequencies in terms of mass and stiffness matrices and an assumed mode shape. The document also discusses exact calculation of natural frequencies and mode shapes by solving the eigenvalue problem of the dynamic matrix. It states that natural frequencies and mode shapes, known as normal modes, are important for qualitative analysis and solving forced vibration problems of MDOF systems.

DOMV No 4 PHYSICAL DYNAMIC MODEL TYPES (1).pdf

This document discusses three physical modeling techniques for dynamic analysis of structures:
1. The lumped-mass procedure simplifies structures by concentrating their mass at discrete points and defining displacements only at those points.
2. The generalized displacement model expresses the deflected shape of a structure as the sum of specified displacement patterns defined by shape functions.
3. The finite-element concept divides structures into elements and expresses displacements in terms of the displacements of nodal points where elements connect, using interpolation functions within each element. All three techniques aim to create a system of differential equations relating mass, damping, stiffness, and external forces.

DOMV No 7 MATH MODELLING Lagrange Equations.pdf

The document discusses mathematical modeling using Lagrange's equations. It begins by introducing Newtonian mechanics, the principle of virtual work, and Lagrange's equations as three approaches. It then focuses on Lagrange's equations, explaining that they describe the dynamics of systems with N degrees of freedom in terms of energy and generalized coordinates. The document provides details on Lagrange's equations, including examples of their use for conservative and dissipative systems. It also discusses how generalized forces are established and the equations of motion for linear multi-degree-of-freedom systems.

DOMV No 2 RESPONSE OF LINEAR SDOF SYSTEMS TO GENERAL LOADING (2).pdf

This document discusses the response of linear single degree of freedom (SDOF) systems to general loading through the use of superposition. It introduces the mass-spring-damper model and defines two special free response functions: the unit amplitude free decay function and the unit velocity free decay function. It explains that the general solution to the forced response of a SDOF system can be constructed by taking a superposition of responses to these two base functions using the initial conditions and applied force over time.

Sensors_2020.pptx

Sensors_2020.pptx

DOMV No 12 CONTINUED ADVANCED KINEMATIC ANALYSIS v2.pdf

DOMV No 12 CONTINUED ADVANCED KINEMATIC ANALYSIS v2.pdf

DOMV No 5 MATH MODELLING Newtonian d'Alembert Virtual Work (1).pdf

DOMV No 5 MATH MODELLING Newtonian d'Alembert Virtual Work (1).pdf

DOMV No 8 MDOF LINEAR SYSTEMS - RAYLEIGH'S METHOD - FREE VIBRATION.pdf

DOMV No 8 MDOF LINEAR SYSTEMS - RAYLEIGH'S METHOD - FREE VIBRATION.pdf

DOMV No 4 PHYSICAL DYNAMIC MODEL TYPES (1).pdf

DOMV No 4 PHYSICAL DYNAMIC MODEL TYPES (1).pdf

DOMV No 7 MATH MODELLING Lagrange Equations.pdf

DOMV No 7 MATH MODELLING Lagrange Equations.pdf

DOMV No 2 RESPONSE OF LINEAR SDOF SYSTEMS TO GENERAL LOADING (2).pdf

DOMV No 2 RESPONSE OF LINEAR SDOF SYSTEMS TO GENERAL LOADING (2).pdf

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三、进国企，银行，事业单位，考公务员等等，这些单位是必需要提供真实教育部认证的，办理教育部认证所需资料众多且烦琐，所有材料您都必须提供原件，我们凭借丰富的经验，快捷的绿色通道帮您快速整合材料，让您少走弯路。
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3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
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我们所定的价格是非常合理的，而且我们现在做得单子大多数都是代理和回头客户介绍的所以一般现在有新的单子 我给客户的都是第一手的代理价格，因为我想坦诚对待大家 不想跟大家在价格方面浪费时间
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二、回国进私企、外企、自己做生意的情况，这些单位是不查询毕业证真伪的，而且国内没有渠道去查询国外文凭的真假，也不需要提供真实教育部认证。鉴于此，办理一份毕业证【微信号:176555708】即可
三、进国企，银行，事业单位，考公务员等等，这些单位是必需要提供真实教育部认证的，办理教育部认证所需资料众多且烦琐，所有材料您都必须提供原件，我们凭借丰富的经验，快捷的绿色通道帮您快速整合材料，让您少走弯路。
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
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7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
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2、国（境）学习人员提供就业推荐信服务
3、留学人员区块链存储服务
【关于价格问题（保证一手价格）】
我们所定的价格是非常合理的，而且我们现在做得单子大多数都是代理和回头客户介绍的所以一般现在有新的单子 我给客户的都是第一手的代理价格，因为我想坦诚对待大家 不想跟大家在价格方面浪费时间
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一、工作未确定，回国需先给父母、亲戚朋友看下文凭的情况，办理一份就读学校的毕业证【微信176555708】文凭即可
二、回国进私企、外企、自己做生意的情况，这些单位是不查询毕业证真伪的，而且国内没有渠道去查询国外文凭的真假，也不需要提供真实教育部认证。鉴于此，办理一份毕业证【微信176555708】即可
三、进国企，银行，事业单位，考公务员等等，这些单位是必需要提供真实教育部认证的，办理教育部认证所需资料众多且烦琐，所有材料您都必须提供原件，我们凭借丰富的经验，快捷的绿色通道帮您快速整合材料，让您少走弯路。
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
留信网服务项目：
1、留学生专业人才库服务（留信分析）
2、国（境）学习人员提供就业推荐信服务
3、留学人员区块链存储服务
→ 【关于价格问题（保证一手价格）】
我们所定的价格是非常合理的，而且我们现在做得单子大多数都是代理和回头客户介绍的所以一般现在有新的单子 我给客户的都是第一手的代理价格，因为我想坦诚对待大家 不想跟大家在价格方面浪费时间
对于老客户或者被老客户介绍过来的朋友，我们都会适当给一些优惠。
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- 1. Response of linear SDOF systems to general loading – use of superposition. Mass-Spring Damper System y is the displacement, in the downward direction, as a result of the force p(t) acting on m p(t) k c m y
- 2. An approach to constructing the general solution for arbitrary forcing
- 3. Linear systems satisfy the principle of superposition (in the Time and Frequency Domains) ?
- 4. Two special free-decay response functions The Unit Amplitude Free-Decay Function
- 5. So what does the UAFD function look like?
- 6. Two special free-decay response functions The Unit Velocity Free-Decay Function
- 7. So what does the UVFD function look like?
- 8. The free response to any set of initial conditions (from superposition) is: ( ) ( ) ( ) y y y t y y t cf UAFD UVFD = + 0 0 ( )
- 9. The Impulse Response function h(t)
- 10. Impulse response Mass-Spring Damper System Consider a unit impulse h(t) applied to a mass- spring-damper system, with light (subcritical) damping parameter ξ (i.e. ξ << 1) and natural frequency ωn . How would it respond? h(t) 2ξωn y
- 11. The Impulse Response function (irf) h(t) (identical to the UVFD function)
- 12. To recap Two functions have been defined: the Unit Amplitude Free Decay Function: 𝑦(𝑡) = 𝑦UAFD(𝑡) and the Impulse Response Function h(t) (which is identical to the Unit Velocity Free Decay Function): 𝑦 𝑡 = h t = 𝑦UVFD 𝑡 We will see in the next lecture that only these two functions are needed to generate the general solution to the forced response of a SDOF system.