Lecture 10 Time Domain Vibration Part 2

Question 1

Laplace transforms allow

Answer 1

differential equations to be replaced by algebraic expressions
and able to handle discontinuous functions eg steps and ramps

Question 2

step by step process of laplace transforms

Answer 2

1. start with differential equations (equation of motion) in time domain
2. Turn into algebraic equations in s domain
3. convert back to solution as a function of time (in time domain)

Question 3

What does the final value theorem state

Answer 3

the final or steady state value of a signal may be written

xss = lim t-> inf x(t) = lim s-> 0 sX(s)

Question 4

What does the initial value theorem state

Answer 4

initial value of a signal is given by

x0 = lim t-> 0 x(t) = lim s->inf sX(s)

Question 5

hat does the final value theorem rely on

Answer 5

validity depends on poles are on the left hand plane and/or a single pole at the origin, ie -ve real component of number