Welcome to PHYSICS –I (PH10001) Sir Isaac Newton Thomas Young Albert Einstein Niels Bohr Werner...

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