# (a) Essay Example

Graphical Methods

Student 9; Asymptotes —

Student 10; Asymptotes —

Student 9;

Student 10;

The voltage across the resistor is given by ;

Substituting the values of ;

The voltage across the inductor is given by

Substituting the values of ;

The voltage across the capacitor is given by

Substituting the values of ;

Numerical Integration

1. (a)

Simpson’s Rule

Trapezoidal Rule

Mid-ordinate Rule

From kelsan online calculator [ CITATION kel17 l 1033 ]–

 % deviation Simpson’s Rule Trapezoidal Rule Mid-ordinate Rule
1. (a) ; n=4

Simpson’s Rule

From Error Function Table –

% deviation = 73.5%

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

Iteration

1. Bisection Method

; ;

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 –

Sonobouy –

1. Square of the distance

1. Equation for minimizing distance

Differentiate wrt x;=

By Newton-Rhapsody method;

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

 2 2.13889 2.12655 -5 0.542639 0.004621 36 43.9737 43.2261 2.13889 2.12655 2.12644

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

 2 1.97973 2.14352 0.75 -5.7187 0.746847 37 34.9152 44.2561 1.97973 2.14352 2.12664