Coriolis Effect on Missiles
Coriolis force on the
missile
a c 2 v sin v
(Taking 300 )
For a cruise missile fired at a target
distant L away, the deviation S is :
1 2 1 L2
s act
2
2 v
For L 10 km, v 7
MEchanics Oscillations and
Waves (MEOW)
D. D. Pant
Associate Professor
Department of Physics
BITS Pilani, Pilani
E-Mail: [email protected]
Office: 3242-L
Major Division
1. Mechanics : 20
BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, Pilani
Pilani Campus
INSTRUCTION DIVISION
SECOND SEMESTER 2014 -2015
Course Handout (Part-II)
Date: 12/01/2015
In addition to part I (General handout for all
Chapter IV
Forced/Driven Oscillations
An additional externally applied harmonic
force acts on the oscillator
Without Damping
d2x
m 2 k x F0 cos t
dt
Or,
d2x
F0
2
0 x cos t
2
dt
m
0 : Natural angular
Chapter V
Coupled Oscillators
and Normal Modes
Two, or more, oscillators coupled together
Examples
1. Two pendulums, coupled by a spring
2. A molecule
CO2 Molecule
3. A crystalline solid
4. An elastic
MEchanics Oscillations and
Waves (MEOW!)
RISHIKESH
VAIDYA
Ph.D.(Theoretical Particle Physics)
Oce: 3265
[email protected]
Physics Group, B I T S
August 2, 2011
Pilani
A Simple Quiz
What is the shap
R.R. Mishra
Department of Physics
Chapter No. 8
Motion in Noninertial
Frames
Motion Looks Different From Different
Frames
Football kicked into the air
Man on the Ground
Man on a Parachute
Bungee Jumpe
Chapter IV
Forced/Driven
Oscillations
An additional externally applied harmonic
force acts on the oscillator
Without Damping
d2x
m 2 k x F0 cos t
dt
Or,
d2x
F0
2
0 x cos t
2
dt
m
0 : Natural angular
Rotating Coordinate System
z
z
(x,y,z) : Inertial frame
y
(x,y,z) : Frame rotating w.r.t
the inertial frame
y
x
x
Goal : Find the equation of motion of a
particle in frame (x,y,z)
Result I
Change in a
Chapter IV
Forced/Driven Oscillations
An additional externally applied harmonic
force acts on the oscillator
Without Damping
d 2x
m 2 k x F0 cos t
dt
Or,
d2x
F0
2
0 x cos t
2
dt
m
0 : Natural angular
Chapter 3
1. Dynamics of a System of Particles &
Conservation of Momentum
2. Centre of Mass & its Motion
3. Centre of Mass coordinates
4. Motion of Systems with Variable Mass
5. Momentum Transport
Dyn
Chapter No. 8
Motion in Noninertial
Frames
Motion Looks Different From Different
Frames
Football kicked into the air
Man on the Ground
Man on a Parachute
Bungee Jumper
A reference frame is a rigid bod
Chapter 7
Progressive
Waves
Waves
Types of Waves
Mathematical description of Waves
Three Velocities in Wave Motion
WAVE MOTION
Motion of infinite coupled oscillators
Transport of Energy without tra
Problem 6.40 and 6.41 Kleppner and Kolenkow
Notes by: Rishikesh Vaidya, Physics Group, BITS-Pilani
6.40 A wheel with ne teeth is attached to the end of a spring with constant k and unstretched length
Prob. 4.7
A ring of mass M hangs
from a thread, and two
m
beads of mass m each
slide on it without
friction. The beads are
released simultaneously
M
from the top of the ring and slide
down opposite si
Chapter IV
Forced/Driven Oscillations
An additional externally applied harmonic
force acts on the oscillator
Without Damping
d 2x
m 2 k x F0 cos t
dt
Or,
d2x
F0
2
0 x cos t
2
dt
m
0 : Natural angular
Mechanics in Noninertial Frames
Why Frames of Reference?
Newtons Equations :
d r
F = ma =m 2
dt
2
are meaningless without frame of reference,
w.r.t which, the position vector, and
consequently the acc
Simple Harmonic Motion
The idealized SHO is a spring-mass
system
F = -kx
Equation of
motion :
2
d x
m 2 k x
dt
O
(The equilibrium
position)
Or,
d2x
2
x 0
2
dt
k
2
m
x
The most general solution of
Chapter V
Coupled Oscillations
Two, or more, oscillators coupled together
Examples
1. Two pendulums, coupled by a spring
2. A molecule
CO2 Molecule
3. A crystalline solid
4. Coupled electrical oscilla
Lectures on Oscillation and waves
By
Kusum Lata
Chamber No. 3242-K
Email Id [email protected]
Mobile No. 09694096462
Text Book: Vibration and Waves by A P French
Reference Book: Waves and
Chapter VI
Angular Momentum & FixedAxis Rotation
Angular Momentum
Angular Momentum of a single particle :
p
r
L=rp
o
For a system of particles :
L
Li
i
ri pi
i
Prob. 6.1
Show that if the total
Chapter IV
Work & Energy
1. Work done by a force :
2. Kinetic Energy & Work-Energy Theorem
3.Conservative Forces and Potential
Energy
4. Potential Energy and Stability
5. Collision
Work done by a forc
Chapter 3
Momentum
1. Dynamics of a System of Particles &
Conservation of Momentum
2. Concept of Centre of Mass
3. Motion of Systems with Variable Mass
Dynamics of a System of Particles &
Conservation
Prob. 6.13
m
Mass m is attached to
m
a post of radius R.
Initially it is at a
distance r0 from the
(b)
(a)
centre of the post and
is moving tangentially
with velocity v0. In case (a) the string passes
Chapter 6
Normal Modes of
Continuous System
The Free Vibrations of
Stretched Strings
Parameters of the string :
Length : L
Tension : T
Density (Linear) :
y
x
When the string vibrates, the displacement
Chapter IV
Work & Energy
1. Work done by a force : Line Integral
2. Kinetic Energy & Work-Energy Theorem
3.Conservative Forces and Potential
Energy
4. Potential Energy and Stability
Work Done by a For