Time Response

Question 1

Values of Laplace variable s that causes the transfer function infinite (based on denominator)

Answer 1

Poles

Question 2

Values of Laplace variable s that causes the transfer function infinite (based on numerator)

Answer 2

Zeros

Question 3

Functions without zeros

Answer 3

first order system

Question 4

the coefficient in response equation (eg. 1)

Answer 4

forced response

Question 5

the other parts of response equation (eg. e^-t, etc.)

Answer 5

natural response

Question 6

General First Order Equation

Answer 6

a/s+a

Question 7

time for e^-at to decay at 37% of initial value

Answer 7

Time constant

Question 8

time it takes for step response to rise to 63% of the final value

Answer 8

Time constant

Question 9

parameter a means

Answer 9

exponential frequency

Question 10

Time constant (Tc) of first order = ?

Answer 10

1/a

Question 11

The initial slope based on first order function = ?

Answer 11

1/Tc = a

Question 12

time for wave to go from 0.1 to 0.9 of final value

Answer 12

Rise Time

Question 13

Rise Time (Tr) for first order = ?

Answer 13

2.2/a

Question 14

time for response to reach and stay within 2% of the final value

Answer 14

Settling Time

Question 15

Settling Time (Ts) = ?

Answer 15

4/a

Question 16

General equation for 2nd Order systems

Answer 16

b/ s^2+as+b

Question 17

When Overdamped response (Distinct & Real Poles = x1, x2)

Answer 17

= A + Be^-x1t +Ce^-x2t

Question 18

When Underdamped response (Complex Poles= x1+- jω)

Answer 18

= A + Be^=x1t cos(ωt-ϕ)

Question 19

When Undamped response (Imaginary Poles= +- jω)

Answer 19

= A + Bcos(ωt-ϕ)

Question 20

When Underdamped response (Repeating/ Real Poles= x1, x1 )

Answer 20

= A + Be^-x1t +Cte^-x1t

Question 21

Frequency of
oscillation of the system without damping

Answer 21

Natural Frequency (ωn)

Question 22

measure of how
oscillations die down after a disturbance

Answer 22

Damping Ratio (ζ)

Question 23

Natural Frequency (ωn)

Answer 23

= sqrt(b)

Question 24

Damping Ratio (ζ)

Answer 24

= a/2(ωn)

Question 25

Equation of 2nd Order with Natural Frequency and Damping Ratio

Answer 25

=(ωn)^2 / s^2 + 2ζ(ωn)s + (ωn)^2

Question 26

ζ > 1

Answer 26

Overdamped

Question 27

ζ = 1

Answer 27

Critically Damped

Question 28

0 < ζ < 1

Answer 28

Underdamped

Question 29

ζ = 0

Answer 29

Undamped

Question 30

Rise Time (Tr) for 2nd Order

Answer 30

Tr = (1.76(ζ)^3 - 0.417(ζ)^2 + 1.039(ζ) + 1) / ωn

Question 31

Peak Time (Tp) for second order, time required to reach the first or max peak

Answer 31

Tp = pi / ωn(sqrt(1-(ζ)^2))

Question 32

Settling Time (Ts)

Answer 32

Ts = 4 / (ζ)ωn

Question 33

% Overshoot, amount in which overshoots the steady state value at peak time as % of steady-state value

Answer 33

e^ -(ζpi /(sqrt(1-(ζ)^2)) x 100