Transcript Lecture 1

Christiaan Huygens
Welcome to
PHYSICS –I (PH10001)
Werner Heisenberg
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 building
Time : 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)
Marks Break-up
Mid semester exam: 30
End semester exam: 50
Tutorial: 20 www.webteam.iitkgp.ernet.in/
physics1
BOOKS
FEYNMAN LECTURES ON PHYSICS VOL I
THE PHYSICS OF VIBRATIONS AND WAVES
by H. J. PAIN
FUNDAMENTALS OF OPTICS
by JENKINS AND WHITE
OPTICS
by EUGENE HECHT
1. LECTURE NOTES & PROBLEMS BANK for
PHYSICS by SARASWAT AND SASTRY
2. PHYSICS I: OSCILLATIONS AND WAVES
by BHARADWAJ AND KHASTAGIR
3. LECTURE NOTE S AND PROBLEMS BANK
by SAYAN KAR at
http://www.cts.iitkgp.ernet.in/Phy_1st/tut.html
Audio lecture:
www.webteam.iitkgp.ernet.in/physics1
Discussion Forum
https://www.facebook.com/groups/523462897801020/
OSCILLATION
HARMONIC OSCILLATION
OSCILLATION
SPRING SIMPLE HARMONIC MOTION
Assumption :
spring is perfectly linear
force of pulling back
 restoring force  -x
m
m
m
x
m
max
x max
HOOKE’S LAW
Equation of motion
2
d x
m 2  kx
dt
k : stiffness constant
Second order ordinary homogenous linear differential eqn.
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
One of the solutions of the differential equation
x  A cos 0t
k
0 
m
A is a constant : Amplitude of motion
o refers to natural motion the spring
Velocity :
dx
v
  a sin t
dt
Acceleration :
2
d x
2
a  2  a cos t
dt
Oscillation!
x
1.0
0.5
0.0
0.0
0.1
0.2
0t
-0.5
-1.0
For A=1
Physical significance of A
A is amplitude of motion
Time pattern of the motion is independent A
Physical significance of 0
cos 0t  cos (0t  2 )
Motion repeats when changes
 0t
: Phase of the motion
 0t
by 2
T: Time period of motion
0T  2
2
m
T
 2
0
k
Phase estimation
x
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
0
T
2
0
t
3
1
2
0  2
For black curve
0  4
For red curve
Shifting the beginning (origin) of the time
General solution
A cos 0 (t  t1 )
Form
t1 = some constant
0: angular freq. (amount of phase change in 1 sec)
(0t+f) : phase of the oscillation
f: phase shift from some defined origin of time
Estimating Amplitude and Phase from Initial conditions
x  D cos 0t  E sin 0t
v  0 D sin 0t  0 E cos 0t
Initial conditions to determine D and E
At t =0
x=x0
and
v=v0
x0  D.1  E.0  D
v 0  0 D.0  0 E.1  0 E
D  x0
E
v0
0
Hence find amplitude
and phase
Velocity :
dx
v
  A0 sin(0t  f )
dt
Acceleration :
2
d x
2
2
a  2   A0 cos(0t  f )  0 x
dt
Potential energy of the spring-mass system
x  A cos(0t  f )
1 2 1 2
2
Potential energy :  kx  kA cos (0t  f )
2
2
1 2
 kA [1  cos 2(0t  f )]
4
Kinetic energy of the spring-mass system
1 2 1
2 2
2
Kinetic energy :  mv  m0 A sin (0t  f )
2
2
1
 m02 A2 [1  cos 2(0t  f )]
4
Total energy of the spring-mass system
Total energy = K.E + P.E
1
2 2
 m0 A
2
Simple Pendulum
Assumption :
massless unstretchable string

0
l
g
ml  mg sin 
 4
sin  
g
   0
l
l
T  2
g
Harmonic and circular motion (only an Analogy)
y
v

Acceleration (a) 
R
X
x  R cos 
y  R sin 
Geometrically
ax  a cos 
 02 R cos   02 x
x component of the displacement of a particle moving along
a circular path with uniform speed is a SHM
•Every oscillatory motion or periodic motion has a frequency
2f
Unit of f : 1Hertz = 1Hz = 1 oscillation/sec =1sec-1
•The period T is the time required for one complete oscillation or cycle
1
T
f
•
Displacement during SHM as a function of time
x  xmax cos(t  f )
xmax: amplitude
•
Velocity during SHM as a function of time
v   xmax sin(t  f )
xmax: velocity amplitude
xmax=A
•
Acceleration during SHM as a function of time
a   xmax cos(t  f )
2
2xmax: acceleration amplitude
FEYNMAN LECTURES ON PHYSICS VOL I
Author : RICHARD P FEYNMAN,
IIT KGP Central Library :
Class no. 530.4