tbd2a.assignment.4 .u28.ausama.2012.border&qs.final1

7/30/2019 TBD2A.assignment.4 .U28.Ausama.2012.Border&Qs.final1

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Sharjah Institute of Technology

Assessment Activity Front Sheet

(This front sheet must be completed by the STUDENT where appropriate and included with the work submitted for assessment)

Students Name: Assessors Name:

Date Issued:Completion

Date:Submitted on: / /

Qualification BTEC National Diploma in Communications Technology -Year 2

Unit No.: 28 Unit Title: Further Mathematics for TechniciansOutcome No. : 4 Outcome Title:

Be able to apply calculus.

Assignment No. : 4Assessment Title: Calculus Techniques and Applications

Part: 1 Of 1

In this assessment you will have opportunities to provide evidence against the following criteria.

Indicate the page numbers where the evidence can be found.

Criteria

Refere

nce

To achieve the criteria the evidence must show that

the student is able to:Tick if

met

Page

numbers

P9Find the differential coefficient for three differentfunctions to demonstrate the use of function of afunction and the product and quotient rules.

P10Use integral calculus to solve two simple engineering

problems involving the definite and indefinite integral.

M3Use differential calculus to find themaximum/minimum for an engineering problem.

D2 Use numerical integration and integral calculus toanalyse the results of a complex engineering problem.

DeclarationI certify that this assignment is my own work, written in my own words. Any other persons work

included in my assignment is referenced / acknowledged.

Students Name: Students Signature: Date:

Internal Verifiers approval to use with students

IVs Name: IVs Signature: Date:

Criteria Achieved

P9 P10 M3 D2

Front Sheet


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Assignment 3 Trigonometric Expressions and Techniques

Scenario

In your work as a Communications technician , you may have todeal with a

variety of calculations and manipulations that need a knowledgeof differential

and integral calculus. As part of your course you are required toprove your

abilities to do such calculations and manipulations through solvingthe following

tasks.

-


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Task 1: [ Pass P9 ]

A.An object moves along the x-axis so that its position at any time, )0( t ,

is given by

( )ttts += 2cos)(

Find the velocity of the object as a function oft.

B.

A ring-shaped conductor with radius R (as shown in the figure above)carries a total charge

(Q) uniformly distributed around it. The electric field at a point P that lies

on the axis of the

ring at a distance x from its center is given by:

( ) 23

224

1

Rx

QxE

o

x

+=

Find the expression for the rate of change of ( xE ) with respect to ( x ),

with the other values being constant.


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C.

In electrostatics, the electric field, ( yE ), at a point P due a line charge isrelated to the

perpendicular distance, ( y ), by the following equation:

( )

+= 21

221 4)4

2( yLyL

Eo

y

Where, oL ,, are constants.

Find the expression for the rate of change of ( yE ) with respect to ( y

).


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Task 2: [ Pass P10 ]

A.

The angular velocity ( ) is the time rate of change of the angulardisplacement ( )

of a rotating object. See the figure above. In testing the shaft of anelectric motor, its

angular velocity is given by:

25016 tt +=

Where (t) is the time of rotation (in seconds).

Find the angular displacement( )

through which the shaft goes in10 seconds.


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B.

A proton is fired at an initial velocity of 150 m/s at an angle of o60 abovethe horizontal

into a uniform electric field as shown in the figure above. Theacceleration (a) due to this

field is, therefore, in the negative y-direction and uniform with a value of24

/1092.1 sm

(the negative sign is chosen so that all quantities directed up are positiveand all quantities

directed down are negative.)

Find the expressions for the y-component of the velocity )( yv and the y-component of

the displacement )( ys for the proton as a function of time (t).

Hint:

dtdva

y

y = , and dtdstv

y=)(


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0)0(

,60cos150)0(

=

=

y

y

s

v

Task 3: [ Merit M3 ]

The magnetic reluctance , ( )R , ofan iron core with a rectangular crosssection is inversely

proportional to the product of its width (w) and its depth (d). (See figureabove.)

Find the dimensions of the iron core with the minimum magneticreluctance that can be

cut from an iron piece with a circular cross section which has a diameter(D =10 2 cm ).


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Task 4: [ Distinct D2 ]

A small mass of metal attached to a spring which is stretched toundergo simple

harmonic motion described by the following equation:

ttv sin3)( =

Where,

=)(tv velocity of mass as a function of time, t. (m/s)

= angular velocity of oscillation. (rad/s)

If the period of oscillation, T, is equal to 2 seconds, find the

displacement of the

mass after ( 1 ) second using:

1. Simpsons Rule; use n = 10

2. Trapezoidal Rule; use n = 10

3. Integral calculus method.

Then find the percentage error of each ofSimpsons Rule and


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Trapezoidal Rule

with respect to the accurate Integral calculus method and

conclude which one is

more accurate.


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Feedback Sheet

Assessment Feedback Form(This feedback sheet must be completed by the ASSESSOR where appropriate)

Students Name:

Unit No.: 28

Assessment Title:

Calculus Techniques andApplications

Unit Title: Further Mathematics for Technicians

Outcome No.: 4

Outcome Title:Be able to apply calculus.

Assignment No.: 4

Part: 1 of 1

Criteria

referenceAssessment Criteria Achieved Evidence Comments/feedback

P9

Find the differential coefficient for threedifferent functions to demonstrate the use offunction of a function and the product andquotient rules.

Yes/NoTask1

Calculations

P10Use integral calculus to solve two simpleengineering problems involving the definite

and indefinite integral.Yes/No

Task2calculations

M3Use differential calculus to find themaximum/minimum for an engineeringproblem.

Yes/NoTask3

calculations

D2 Use numerical integration and integralcalculus to analyse the results of a complexengineering problem.

Yes/NoTask4

calculations

Assessors General Comments:

Assessors Name: Ausama Ibrahim Hassan Signature: Date:

Students Comments:

Students Name: Signature: Date:

Student's Work has been Internally Verified

IVs Name: Waleed IVs Signature: Date:

Criteria Achieved

P9 P10 M3 D2


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