Electromagnetic Wave Propagation Lecture 4: Propagation in ...
Vol. 3 Main Contents ： 1.Vibration 2.Wave---Propagation of vibration or field. 3.Wave...
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Transcript of Vol. 3 Main Contents ： 1.Vibration 2.Wave---Propagation of vibration or field. 3.Wave...
3.Wave optics---Propagation of light
4. Special theory of relativity---The theory for high speed motion.
5. Quantum physics---The theory for the motion of microscopic bodies.
Chapter 14 Vibration
§14-5 Superposition of SHM
IV.Characteristic quantities of SHM
Initial PA
0
M0
M
x
—Rotating vector
[Example] Spring k, dish M are at rest when t=0. Prove that the motion of m+M is SHM after m falls down to the dish and find the kinematic equation.
Prove
Choose the origin point 0 is at the point that the resultant force acting on M+ m is zero.
Gravity, elastic force
Analyse the forces acting on M+ m
then
h
m
0
x
A, are determined by initial conditions
So we can get
As x0<0v0>0, we can get that < < 3 /2
kinematic equation
Aaxis
physical …
0
m
A
c
h
mg
Angular
acceleration
PP
SP
Restoring
torque
Dynamics
Eq.
Here
Dyn.Eq.
Conclusions
The “period” of damped Vibr
3.Critically dampedb = w0
We get
The object returns to equilibrium position with no oscillation in the shortest time possible.
Critically damped
Let
Underdamped (b < w0 )
--- SHM
substitute
As w w0A is larger
A getting larger as
Let
We get
The angular frequency of resonance r = the angular frequency of driving force when the system is at resonance.
Note
Energy loss is larger.
§14-3 Superposition of SHM
I. Superposition Principle of vibration
If an object participates two or more vibrations simultaneously, the resultant position of the object at any time is equal to the vector sum of the positions produced by each of the vibrations separately.
II. Superposition of two SHM with same direction and same frequency
1. Algebraic solution
The initial phase of resultant vibration
2. Rotating Vector solution
destruction
III. Superposition of two SHM with same direction and different frequency
Separate vibrations
Resultant vibration
When
Separate vibrations
Resultant vibration
Ellipse equation
V. Superposition of two perpendicular SHM with different frequency
If the frequency ratio of the two perpendicular SHM has simple integral relation, the path of the resultant vibration is called as Lissajous curves( )
26223.bin
k
b
1
4. Special theory of relativity---The theory for high speed motion.
5. Quantum physics---The theory for the motion of microscopic bodies.
Chapter 14 Vibration
§14-5 Superposition of SHM
IV.Characteristic quantities of SHM
Initial PA
0
M0
M
x
—Rotating vector
[Example] Spring k, dish M are at rest when t=0. Prove that the motion of m+M is SHM after m falls down to the dish and find the kinematic equation.
Prove
Choose the origin point 0 is at the point that the resultant force acting on M+ m is zero.
Gravity, elastic force
Analyse the forces acting on M+ m
then
h
m
0
x
A, are determined by initial conditions
So we can get
As x0<0v0>0, we can get that < < 3 /2
kinematic equation
Aaxis
physical …
0
m
A
c
h
mg
Angular
acceleration
PP
SP
Restoring
torque
Dynamics
Eq.
Here
Dyn.Eq.
Conclusions
The “period” of damped Vibr
3.Critically dampedb = w0
We get
The object returns to equilibrium position with no oscillation in the shortest time possible.
Critically damped
Let
Underdamped (b < w0 )
--- SHM
substitute
As w w0A is larger
A getting larger as
Let
We get
The angular frequency of resonance r = the angular frequency of driving force when the system is at resonance.
Note
Energy loss is larger.
§14-3 Superposition of SHM
I. Superposition Principle of vibration
If an object participates two or more vibrations simultaneously, the resultant position of the object at any time is equal to the vector sum of the positions produced by each of the vibrations separately.
II. Superposition of two SHM with same direction and same frequency
1. Algebraic solution
The initial phase of resultant vibration
2. Rotating Vector solution
destruction
III. Superposition of two SHM with same direction and different frequency
Separate vibrations
Resultant vibration
When
Separate vibrations
Resultant vibration
Ellipse equation
V. Superposition of two perpendicular SHM with different frequency
If the frequency ratio of the two perpendicular SHM has simple integral relation, the path of the resultant vibration is called as Lissajous curves( )
26223.bin
k
b
1
