Further Analytical Methods for Engineers Essay Example

Introduction

This paper consist of 5 tasks. In tasks 1 focus was on errors. In tasks 1.2 there was solution of problem involving conversion from binary to octal and hexadecimal number systems. In tasks 1.2 there is also a question on drawing a truth table. The other three tasks majorly involved complex number algebra.

Task (LO 1.1)

, where ) of an ideal gas are obtained using the equation The number of moles (

is the pressure measured in Pascals (Pa),

is the volume measured in cubic metres (m³),

is the universal gas constant (8.31447JK^-1mol^-1),

is the temperature measured in Kelvin (K)

In a repeated experiment, the temperature of the gas was measured by a digital meter to the nearest Celsius. The following repeated measurements were obtained :

32C, 33C, 32C, 34C, 32C, 33C, 32C, 32C, 32C, 31C

1. What is the uncertainty due to the reading error of the digital meter

2. ) or Calculate the uncertainty due to the random error of the repeated measurements (you can either use standard error =

3. Calculate the mean of the of the repeated measurements and round off to an appropriate number of significant figures

4. .
   and explain the choice of your uncertainty , Conclude on the uncertainty in the temperature measurements i.e. express in the form

The temperature of the gas must be in Kelvin before it is used in the equation . This is obtained by adding 273 to the Celsius temperature. The measured values of the other quantities are:

Pa

cm³

JK^-1mol^-1

5. with its uncertainty given to an appropriate number of significant figures. Calculate the value of

Maximum possible value

Minimum possible value

Uncertainty

Task (LO 1.2)

1. Convert the binary 1101 1110 1010 1101 into

0	0	0	0	0
0	0
0		0
0
	0	0
	0
		0

From the table1 it can be seen that you need 3 cells to represent any possible digit in octal number octal number

We divide the binary numbers into 3 cells to and represent each in octal starting from left. We give each of the 3 cell binomial number its octal equivalent according to table 1.

Thus the octal number =157255

2. hexadecimal

	Hexadecimal
0	0	0	0	0	0
0	0	0
0	0		0
0	0
0		0	0
0		0
0			0
0
	0	0	0
	0	0
	0		0
	0
		0	0
		0
			0

From the table3 it can be seen that you need 4 cells to represent any possible digit in hexadecimal number

We divide the binary numbers into 4 cells to and represent each in hexadecimal digit starting from left. We give each of the 4 cell binomial number its hexadecimal equivalent according to table 4.

Thus the hexadecimal number is DEAD

1. Draw a truth table to determine the output states at Z with all possible combinational input states at A, B, C & D.

0	0	0	0	0
0	0	0
0	0		0
0		0	0	0
		0	0	0
			0	0
			0	0
				0

Task (LO 1.3)

Two complex numbers are such that and

1. . and the principal in rectangular (Cartesian) form. Now, findWrite down

Substituting with assigned values

2. into polar form i.e. in the form and Convert

rad

In polar form

rad

In polar form

3. in rectangular (Cartesian ) form. . Now, write and the principalFind

Principal

Task (LO 1.4)

using De Moivre’s theorem in rectangular (Cartesian) form. Where m is given by 3 + n modulo 5 and n is your dataset number.Find the m complex roots of the equation

][For example, for n=9 then n modulo 5 = 9 modulo 5 = 4. Therefore 3 + n modulo 5 = 3+4 = 7. And the question would be to find the 7 roots of

2 modulo 5 =7

Therefore 3+nmodulo 5 =3+7=10

From De Moivre’s theorem

Task (LO 1.5)

is the frequency of the alternating power supply, measured in Hertz (Hz). and , where The complex impedance of a circuit containing a resistor of resistance R, inductor of inductance L and a capacitor of capacitance C is given by

1. to an appropriate number of significant figures the impedance

Making substitutions

to an appropriate number of significant figures

Conclusion

The solution of all the tasks were successfully found