Page 106 - MATLAB an introduction with applications

MATLAB Basics ——— 91

Determine the change in the potential energy of a satellite with a mass of 500 kg that is raised from the surface
of the earth to a height of 800 km.
P1.35: Find the Laplace transform of the following function using MATLAB:
3
f (t) = 7t cos(5t + 60°)
P1.36: Use MATLAB program to find the transforms of the following functions.
(a) f (t) = –7t e –5t
(b) f (t) = –3 cos 5t
(c) f (t) = t sin 7t
(d) f (t) = 5 e –2 t cos 5t
(e) f (t) = 3 sin(5t + 45º)
–3t
(f ) f (t) = 5 e cos(t – 45º)
P1.37: Consider the two matrices
 1 0 2  7 8 2

A =   2 5 4 and B =   3 5 9  

− 18 7  − 1 3 1 


Using MATLAB, determine the following:
(a) A + B
(b) AB
(c) A 2
(d) A T
(e) B –1
T T
(f ) B A
2
2
(g) A + B – AB
(h) determinant of A, determinant of B and determinant of AB.
P1.38: Use MATLAB to define the following matrices:
 21 5 3   2 3 



A =   05 , B =   − 2 − 4  , C = − 5 − 2 , D = [1 2]



  74      0 3  
Compute matrices and determinants if they exist.
T –1
(a) (AC )
(b) |B|
T
(c) |AC |
T
(d) (C A) –1
P1.39: Consider the two matrices
 1 0 1  7 4 2
A=   2 3 4   and B =   3 5 6  
− 16 7  − 1 2 1 



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