Welcome toPHYSICS –I (PH10001)

Sir Isaac Newton Thomas Young

Albert Einstein

Niels Bohr Werner Heisenberg

Christiaan Huygens

Course Content

Oscillations – 8 lectures Waves - 8 lectures Interference - 7 lectures Diffraction - 7 lectures Polarisation - 4 lectures Quantum Physics - 8 lectures

L-T-P 3-1-0

Instructor: Dr. Anushree Roy

Contact number : 83856

Availability :Venue: Room No. C133 in main buildingTime : Thursday 5.00-6.30 pm

Slides other details available at: www.webteam.iitkgp.ernet.in/physics1

Class Timings

Monday: From 1.30 to 2.30(door will close at 1.40) Tuesday: From 3.30 to 5.30(door will close at 3.45)

Mid semester exam: 30

End semester exam: 50

Tutorial: 20 

Marks Break-up

www.webteam.iitkgp.ernet.in/physics1

BOOKS

FEYNMAN LECTURES ON PHYSICS VOL I

THE PHYSICS OF VIBRATIONS AND WAVESby H. J. PAIN

FUNDAMENTALS OF OPTICSby JENKINS AND WHITE

OPTICSby EUGENE HECHT

1. LECTURE NOTES & PROBLEMS BANK forPHYSICS by SARASWAT AND SASTRY

3. LECTURE NOTE S AND PROBLEMS BANKby SAYAN KAR at

http://www.cts.iitkgp.ernet.in/Phy_1st/tut.html

Audio lecture: www.webteam.iitkgp.ernet.in/physics1

2. PHYSICS I: OSCILLATIONS AND WAVES by BHARADWAJ AND KHASTAGIR

Discussion Forum

https://www.facebook.com/groups/523462897801020/

OSCILLATION

HARMONIC OSCILLATION

OSCILLATION

SPRING SIMPLE HARMONIC MOTION

Equation of motion

2

2

d xm kx

dt

mm

mm

xmax

max

Assumption : spring is perfectly linear

force of pulling back restoring force -x

xHOOKE’S LAW

k : stiffness constant

second order: because the highest derivative is second order.

ordinary: because the derivatives are only with respect to one variable (t).

homogeneous: because x or its derivatives appear in every term, and

linear: because x and its derivatives appear separately and linearly in each term

Second order ordinary homogenous linear differential eqn.

One of the solutions of the differential equation

0cosx A t

0

k

m

A is a constant : Amplitude of motion

wo refers to natural motion the spring

Velocity :

Acceleration :

tadt

dx sinv

tadt

xd cosa 22

2

Oscillation!

For A=1

0.0 0.1 0.2

-1.0

-0.5

0.0

0.5

1.0

0t

x

Time pattern of the motion is independent A

A is amplitude of motion

Physical significance of A

0 0cos cos ( 2 )t t

Motion repeats when changes by 2p

: Phase of the motion

t0

t0

Physical significance of w0

0 2T

T: Time period of motion

0

22

mT

k

Phase estimation

0

2

T

0 1 2 3-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

0 1 2 3-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

t

x

20 For black curve

For red curve 40

Shifting the beginning (origin) of the time

General solution

t1 = some constant

0 1cos ( )A t t Form

1010

00

10

0

10

sin coswith

sincos

where

)cos(

)(cos

tAEtAD

tEtDx

t

tAx

ttAx

w0: angular freq. (amount of phase change in 1 sec)

(w0t+f) : phase of the oscillation

f: phase shift from some defined origin of time

0 0

0 0 0 0

cos sin

v sin cos

x D t E t

D t E t

Initial conditions to determine D and E

At t =0 x=x0 and v=v0

0

0 0 0 0

0

0

0

.1 .0

v .0 .1

v

x D E D

D E E

D x

E

Estimating Amplitude and Phase from Initial conditions

Hence find amplitude and phase

Velocity :

Acceleration :

0 0v sin( )dx

A tdt

22 2

0 0 02cos( )

d xa A t x

dt

0cos( )x A t

Potential energy of the spring-mass system

Potential energy :2 2 2

0

20

1 1cos ( )

2 21

[1 cos 2( )]4

kx kA t

kA t

Kinetic energy of the spring-mass system

Kinetic energy :2 2 2 2

0 0

2 20 0

1 1v sin ( )

2 21

[1 cos 2( )]4

m m A t

m A t

Total energy = K.E + P.E 2 20

1

2m A

Total energy of the spring-mass system

Assumption : massless unstretchable string

Simple Pendulum

sin

4 sin

ml mg

0

2

g

l

lT

g

0

m

q

l

g

Harmonic and circular motion (only an Analogy)

Acceleration (a) R20

cos

sin

x R

y R

Geometrically

cosxa a 2 20 0cosR x

x component of the displacement of a particle moving along a circular path with uniform speed is a SHM

qR

X

yv

•Every oscillatory motion or periodic motion has a frequency=2w pf

Unit of f : 1Hertz = 1Hz = 1 oscillation/sec =1sec-1

•The period T is the time required for one complete oscillation or cycle

1T

f

•Displacement during SHM as a function of time

maxx cos( )x t xmax: amplitude

•Velocity during SHM as a function of time

•Acceleration during SHM as a function of time

maxv sin( )x t

wxmax: velocity amplitude

2max cos( )a x t

w2xmax: acceleration amplitude

xmax=A

FEYNMAN LECTURES ON PHYSICS VOL I

Author : RICHARD P FEYNMAN,

IIT KGP Central Library :

Class no.  530.4