(a) Essay Example

Graphical Methods

Student 9; Asymptotes — (a)

(a) 1

Student 10; Asymptotes — (a) 2

(a) 3

(a) 4

(a) 5

(a) 6

(a) 7

(a) 8

(a) 9

(a) 10

(a) 11

Student 9; (a) 12

(a) 13

Student 10; (a) 14

(a) 15

(a) 16

(a) 17

The voltage across the resistor is given by (a) 18 ; (a) 19

Substituting the values of (a) 20 ;

(a) 21

The voltage across the inductor is given by (a) 22

Substituting the values of (a) 23 ;

(a) 24

The voltage across the capacitor is given by (a) 25

Substituting the values of (a) 26 ;

(a) 27

Numerical Integration

  1. (a) (a) 28

Simpson’s Rule

(a) 29

(a) 30

Trapezoidal Rule

(a) 31

(a) 32

Mid-ordinate Rule

(a) 33

(a) 34

From kelsan online calculator [ CITATION kel17 l 1033 ]–

% deviation

Simpson’s Rule

(a) 35

Trapezoidal Rule

(a) 36

Mid-ordinate Rule

(a) 37

  1. (a) (a) 38 ; n=4

Simpson’s Rule

(a) 39

(a) 40

From Error Function Table – (a) 41

% deviation = 73.5%

The accuracy of the Simpson’s Rule above can be increased by increasing the number of segments

Iteration

  1. Bisection Method

(a) 42 ; (a) 43 ; (a) 44

(a) 45

Using the interval [0, π]

c=0.5(a+b)

180.00000

-56.30173

90.00000

-27.62925

90.00000

90.00000

-27.62925

45.00000

-13.30788

45.00000

45.00000

-13.30788

22.50000

-6.16918

22.50000

22.50000

-6.16918

11.25000

-2.59668

11.25000

11.25000

-2.59668

-0.80048

-0.80048

  1. Closest Point of Approach

Point on submarine path –(a) 46

Sonobouy – (a) 47

  1. Square of the distance

(a) 48

(a) 49

(a) 50

  1. Equation for minimizing distance

(a) 51

Differentiate wrt x;=

(a) 52

By Newton-Rhapsody method;

Student 9 (a, b)=(4, -1)

(a) 53

(a) 54

2.000000

2.138889

2.126549

-5.000000

0.542639

0.004621

36.000000

43.973680

43.226092

2.138889

2.126549

2.126442

(a) 55

Student 10 (a, b)=(3.5, -1)

(a) 56

(a) 57

2.000000

1.979730

2.143518

0.750000

-5.718702

0.746847

37.000000

34.915233

44.256129

1.979730

2.143518

2.126642

(a) 58