Quiz 2

Time Constant

Equal to 1/a; Equal to 1/(zeta)(natural frequency) the exponential decay component of a signal of the form [form here] for some constants and a

Order

Highest derivative in an DE, or in a system, is the sum of the nth derivatives

Response

Output(s) of a system because of an initial condition and/or input.

Critically Damped

a damping value that is equal to the critical damping value.

Overdamped

a damping value that is greater than the critical damping value and will not oscillate.

Underdamped

a damping value that is less than the critical damping value and will oscillate.

Constant Coefficient

a differential equation in which all coefficients of the dependent variable are independent of the independent variable.

Variable Coefficient

a differential equation in which at least one of the coefficients of the dependent variable is a function of the independent variable.

Impulse

a mathematical function designed to represent an input that is applied for an infinitesimal time (i.e: impact)

Equilibrium

a state of the system that will not change except if disturbed from the state by an input.

Proper Transfer Function

a transfer function in which the degree (order) of the numerator is less than or equal to the degree of the denominator.

Dependent Variable

a variable in an equation that depends on the value of one or more other variables.

Independent Variable

a variable in an equation which does not depend on the value of other variables.

Ordinary Differential Equation (ODE)

an equation consisting of derivatives of a function of a single dependent variable, functions of the dependent variable, and constants.

Rational Function

any function that can be defined as a ratio of polynomials

Characteristic Polynomial

denominator of the transfer function

Homogenous

differential equation is a linear differential equation with no constant term.

Strictly Proper Transfer Function

is one in which the degree (order) of the numerator is strictly less than the degree of the denominator.

Characteristic Equation

results of setting the characteristic polynomial equal to zero.

Transfer Function

the Laplace transform of the output divided by the Laplace transform of the input of the system, assuming zero initial conditions.

Stability

the characteristic of a system that has a bounded output for any bounded input (BIBO stability). The free response of a stable system approaches zero.`

Damping

the decrease in the magnitude of the oscillations of a system due to the removal of energy from the system

Normal Form

the form in which the coefficient of the highest power of s in the denominator is one.

Damped Natural Frequency

the frequency at which the free response of an damped system tends to oscillate

Natural Frequency

the frequency at which the free response of an undamped system tends to oscillate (i.e. no input or damping).

Forced Response

the part of response due to the forcing function (i.e. input). If the input is zero, there is none.

Transient Response

the part of the response that disappears (decays to zero) with time.

Free Response

the part of the response that is due to the initial condition. If the initial conditions are zero, there is none.

Steady State Response

the part of the response that remains with time.

Damping Ratio

the ratio between the damping in a system and the critical damping value of the system

Initial Condition

the state of a system at the initial time.

Complete Response

the sum of the free and forced response. It is also the sum of the steady-state and transient response.

Critical Damping

the value that is just sufficient to prevent oscillations

Dominant Roots

those that result in the longest lasting terms in the transient response (those with the smallest real parts).