Matlab 4 Questions

SYST 221: Systems Modeling Laboratory Problem Set

- Use the file name convention: LastNameFirstName_W4 - Problems in blue are for classroom practice.

Problem 1

Solve the following differential equations:

(i)

(ii)

(iii)

Problem 2 (3 points)

Solve the following differential equations where the input is f(t) = 5t and the initial conditions are zero. Plot the response of the following models for 0 ≤ t ≤ 1.5

(i)

(ii)

(iii)

Problem 3

Obtain the Laplace transform of the following function:

  10cos(2t) x(t)

be ae - 2 x(t)

t x(t)

3t-2t-







Problem 4 (2 points)

Calculate the Laplace transform of the following function:

Problem 5

2 12 dy

y dt

  (0) 10y 

2 2 ( ) 3 sin 5 4 cos 5

t t v t e t e t

   

W4

2

2 3 2 24

d y dy y

dt dt    (0) 10y  '(0) 0y 

2

2 2 5 20

d y dy y

dt dt    (0) 0y  '(0) 10y 

Calculate the inverse transform of the following functions:

(i)

(ii)

(iii) Expand the following transform using Partial-Fraction expansion. Also calculate the inverse transform.

Problem 6 (2 points)

Obtain the inverse Laplace transform x(t) for each of the following transforms:

(i)

(ii)

Problem 7 (3 points)

Solve the following problems:

(i)

(ii) 5

2

100( 3) ( )

( 1)( 2)( 2 5)

s F s

s s s s

 

   

2

10 48 ( )

2 ( 2)( 16) Y s

s s s  

  