July 2013

PHE-02 ASSIGNMENT BOOKLET Bachelor’s Degree Programme (B.Sc.) OSCILLATIONS AND WAVES

Valid from July 1, 2013 to March 31, 2014

It is compulsory to submit the Assignment before filling in the Term-End Examination Form.

Please Note • You can take electives (56 to 64 credits) from a minimum of TWO and a maximum of FOUR science disciplines, viz. Physics, Chemistry, Life Sciences and Mathematics. • You can opt for elective courses worth a MINIMUM OF 8 CREDITS and a MAXIMUM OF 48 CREDITS from any of these four disciplines. • At least 25% of the total credits that you register for in the elective courses from Life Sciences, Chemistry and Physics disciplines must be from the laboratory courses. For example, if you opt for a total of 64 credits of electives in these 3 disciplines, at least 16 credits should be from lab courses. • You cannot appear in the Term-End Examination of any course without registering for the course. Otherwise, your result will not be declared and the onus will be on you.

School of Sciences Indira Gandhi National Open University Maidan Garhi, New Delhi-110068 (For July, 2013 Cycle)

Dear Student, We hope you are familiar with the system of evaluation to be followed for the Bachelor’s Degree Programme. At this stage you may probably like to re-read the section on assignments in the Programme Guide for Elective Courses that we sent you after your enrolment. A weightage of 30 per cent, as you are aware, has been earmarked for continuous evaluation which would consist of one tutor-marked assignment for this course. Instructions for Formatting Your Assignments Before attempting the assignment, please read the following instructions carefully. 1) On top of the first page of your TMA answer sheet, please write the details exactly in the following format:

ENROLMENT NO.:…………………………………………… NAME :…………………………………………… ADDRESS :…………………………………………… …………………………………………… …………………………………………… COURSE CODE:

…………………………….

COURSE TITLE :

…………………………….

ASSIGNMENT NO. ………………………….… STUDY CENTRE:

………………………..…..

DATE:.…………………………………………...

PLEASE FOLLOW THE ABOVE FORMAT STRICTLY TO FACILITATE EVALUATION AND TO AVOID DELAY. 2) Use only foolscap size writing paper (but not of very thin variety) for writing your answers. 3) Leave 4 cm margin on the left, top and bottom of your answer sheet. 4) Your answers should be precise and in your own words. Do not copy answers from study material. 5) While solving problems, clearly indicate the question number along with the part being solved. Write units at each step of your calculations as done in the text because marks will be deducted for such mistakes. Take care of significant digits in your work. Recheck your work before submitting it. 6) This assignment will remain valid from July 1, 2013 to March 31, 2014. However, you are advised to submit it within 12 weeks of receiving this booklet to accomplish its purpose as a teaching-tool. Answer sheets received after the due date shall not be accepted. We strongly feel that you should retain a copy of your assignment response to avoid any unforeseen situation and append, if possible, a photocopy of this booklet with your response. If you have any problems or queries related to the course, you can write to us on the e-mail [email protected] or [email protected]. We wish you good luck. 2

Tutor Marked Assignment PHE-02: Oscillations and Waves Course Code: PHE-02 Assignment Code: PHE-02/TMA/2013-14 Max. Marks: 100

Note: Attempt all questions. Symbols have their usual meanings. The marks for each question are indicated against it.

1. a) Write the equation of motion of a simple harmonic oscillator which has an amplitude of 5 cm and it executes 150 oscillations in 5 minutes with an initial phase of 45°. Also obtain the value of its maximum velocity. (3+2) b) If the displacement of a particle executing SHM be 10 cm and 12 cm when the −1 −1 corresponding velocities are 16 cms and 14 cms respectively, calculate the amplitude of motion. (5) c) Derive expressions for potential energy and kinetic energy of an oscillating spring-mass system. (5+5) d) Discuss the principle of superposition. Two collinear SHMs, with amplitudes 5 cm and 12 cm are superposed. Calculate the resultant amplitude when the SHMs differ in phase by (i) 60°, (ii) 90° and (iii) 120°. (4+6) e) Establish the differential equation for a damped oscillator. Show that, for weak damping, the solution of the differential equation for the damped oscillator is given by x(t ) = a0 exp (− bt ) cos (ωd t + φ)

(4+6)

f) What do you understand by weakly damped forced oscillator and its transient and steady states? Show that the average power absorbed by a forced oscillator is given by  bF 2  ω2

= 0   m  [(ω2 − ω2 ) 2 + 4b 2 ω2 ] 0  

(5+5)

g) What do you understand by the normal modes of coupled oscillators ? If a coupled system has many normal modes, do all normal modes have the same frequency? Calculate the velocity of elastic longitudinal wave along a stretched steel wire, given −3 11 −2 density of steel = 8000 kgm , Young’s modulus of elasticity = 2×10 Nm . (3+2+5) 2. a) Two points x1 and x2 at x = 0 and x = 1 m are observed. The transverse motion of the two points are found to be as follows:

y1 ( x, t ) = 0.2 sin 3πt and

π  y2 ( x, t ) = 0.2 sin  3πt +  8 

Calculate the frequency, wavelength and speed of the wave.

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(5)

b) A sinusoidal wave is described by y ( x, t ) = 4.0 sin (4.20 x − 5.95 t ) cm

where x is the position along the wave propagation. Determine the amplitude, wave number, wavelength, frequency and velocity of the wave. (2×5 = 10) c) Two waves, travelling along the same direction, are given by y1 ( x, t ) = a sin (ω1t − k1 x) and

y2 ( x, t ) = a sin (ω2t − k 2 x)

Suppose that ω1 and k1 are respectively slightly greater than ω2 and k2. (i) Derive an expression for the resultant wave obtained by their superposition. (ii) Explain the formation of wave packet. (5+5) d) Standing waves are produced by the superposition of two waves given by y1 ( x, t ) = 0.2 sin π (t − 2 x) m

and

y2 ( x, t ) = 0.2 sin π (t + 2 x) m

(i) Obtain the resultant displacement of the particle at x at time t. (ii) At what value of x is displacement zero at all times. (iii) What is the distance between two nearest values of x at which the displacement is zero. Is it related to wavelength? (3+3+4) e) A 125 cm long string has a mass 2.0 g and it is stretched with a tension of 7.0 N between fixed supports. What is the speed of the transverse wave on the string? (5) ******

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TENTATIVE SCHEDULE FOR PHYSICS PROGRAMMES BROADCAST ON GYAN DARSHAN 1 July 2013 – May 2014 This is the tentative schedule for Physics students. The students may approach their cable operator to avail this facility. Date/Day July 2013 07-07-13 (Sun) 09-07-13 (Tues) 14-07-13 (Sun) 21-07-13 (Sun) 23-07-13 (Tues) August 2013 06-08-13 (Tues) 13-08-13 (Tues) 20-08-13 (Tues) 27-08-13 (Tues)

Time Slot

Course Code

Video Programme Title

9.00-9.30 pm

PHE-04

Vector Calculus Part-I

8.30-9.00 am

BPHE-101

9.00-9.30 pm

PHE-11

Exploring Physics: Experiments with Low cost Materials Matter Waves and the Uncertainty Principle

9.00-9.30 pm

PHE-11

Wave Particle Duality

8.30-9.00 am

BPHE-101

The Bicycle: A Vehicle for Teaching Physics

8.30-9.00 am

BPHE- 101

The Physics of Dance

8.30-9.00 am

PHE- 15

The Milky Way

8.30-9.00 am

PHE -04

Vector Calculus Part-II

8.30-9.00 am

PHE- 15

Stellar Spectra and Classification

PHE- 10

Digital Modulation

PHE -10

Amplitude Modulation

PHE- 06

First Law of Thermodynamics

PHE-06

Applications of the First Law of Thermodynamics

PHE-15

Stellar Structure

PHE-10

Transistor Biasing

PHE-06

Thermodynamics in Action

PHE-06

Ushmagatiki ke Anuprayog

PHE-10

Electronic Devices

September 2013 03-09-13 8.30-9.00 am (Tues) 08-09-13 9.00-9.30 am (Sun) 10-09-13 8.30-9.00 am (Tues) October 2013 06-10-13 9.00–9.30 pm (Sun) 13-10-13 9.00–9.30 pm (Sun) November 2013 10-11-13 9.00–9.30 pm (Sun) December 2013 15-12-13 9.00–9.30 pm (Sun) 17-12-13 8.30-9.00 am (Tues) 24-12-13 8.30-9.00 am (Tues)

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Date/Day

Time Slot

Course Code

Video Programme Title

9.00–9.30 pm

PHE-15

Glimpses of the Cosmos

9.00–9.30 pm

PHE-02

Simple Harmonic Motion

9.00–9.30 pm

PHE-15

Exploring the Night Sky

8.30-9.00 am

PHE-02

Dolan

9.00–9.30 pm

PHE-15

On the Trail of Stars

8.30-9.00 am

PHE-06

Second Law of Thermodynamics

8.30-9.00 am

PHE-02

Coupled Oscillations

8.30-9.00 am

PHE-13

Introduction to Crystal Structure

8.30-9.00 am

PHE-15

Astronomical Coordinates

9.00–9.30 pm

PHE-10

Operational Amplifier

8.30-9.00 am

PHE-06

Carnot Cycle

9-00-9.30 pm

PHE-15

Astronomical Measurements (Measurement of Distance and Brightness)

9-00-9.30 pm

BPHE-101

Rotating Frames of Reference

9.00-9.30 pm

PHE-15

Astronomical Measurements (Measurement of Mass, Temperature and Time)

8.30-9.00 am

BPHE-101

Logic Gates

January 2014 05-01-14 (Sun) 12-01-14 (Sun) 19-01-14 (Sun) 21-01-14 (Tues) February 2014 02-02-14 (Sun) 04-02-14 (Tues) 11-02-14 (Tues) March 2014 04-03-14 (Tues) 11-03-14 (Tues) 16-03-14 (Sun) 18-03-14 (Tues) April 2014 06-04-14 (Sun) 13-04-14 (Sun) May 2014 11-05-14 (Sun) 13-05-14 (Tues)

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TENTATIVE SCHEDULE FOR PHYSICS STUDENTS ON DD1 (National Network) JULY 2013 TO MAY 2014 Time: 6.00 AM to 6.30 AM July 2013

PHE-10

Operational Amplifier

PHE-02

Coupled Oscillations

PHE-10

Transistor Configuration

PHE-06

Thermodynamics in Action

PHE-15

Exploring the Night Sky

PHE-13

Introduction to Crystal Structure

08-07-13 August 2013 12-08-13 September 2013 09-09-13 October 2013 14-10-13 November 2013 11-11-13 January 2014 13-01-14 February 2014

BPHE-101

Ghurni Nirdesh Tantra (Hindi)

10-02-14 March 2014

PHE-15

The Milky Way

PHE-10

Semiconductor Diode

PHE-15

On the Trail of Stars

10-03-14 April 2014 14-04-14 May 2014 12-05-14 * Second Monday of every month

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