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Phys 211 Vibration and Waves
Main Lecture: MWF 10:10-11:00 Sharp 100
John ClemOffice SHL 201, Hrs 11-12 MWF
Labs: (Starts on the 20th)
F 10:10-11:00 Sharp 114
There will be a lecture this Friday.
Link is posted on Sakai
http://www.bartol.udel.edu/~clem/phys211spr15/Phys211Spring2015.htmsyllabus
2This course is on Waves and VibrationsOscillations and Periodic Events
Periodic PhenomenaHeart beat Breathing Blinking Daily routines EatingSleeping Going to ClassesStream of liquid
while Drinking
Water wavesBouncing BuoyMotion of electrons
and atoms SeasonsOrbits of planetsVisible light and
radio sound
3When I talk my vocal cords vibrate, modulating the flow of air being expelled from the lungs
Sound waves causes the ear drums to vibrate and sends an electrical signal to the brain
OscillationsaboutEquilibrium
4
The basic cause of oscillations is the fact that when an object is displaced from a position of stable equilibrium it experiences a restoring force that is directed back toward the equilibrium position.
FF
5If you run around a track six times in one hour at a constant speed, how long did it take you to complete just one lap?
Six cycles per hour is the frequency and one sixth of an hour (or ten minutes) is the period.
Period T : time required for one cycle of periodic motion
Frequency f : number of oscillations per unit time
Angular Frequency : number of radians per unit time
Parameters
6Simple harmonic motion occurs when therestoring force is proportional to the displacementfrom equilibrium. For example the spring
We can not use our kinematic equations since acceleration is not constant
So what is this motion?
7yr
y = r sin
= t
y = r sin t
Demonstration
Rotating wheel with a rod attached near the edge
But what is ?
angular frequency
IN SHM, the amplitude A is the maximum displacement from equilibrium.
Position as a function of time:
Velocity as a function of time:
Acceleration as a function of time:
8
The angular frequency of a Mass on a SpringSince the force on a mass on a spring is proportional to the displacement, and also to the acceleration, we find that .
Substituting the time dependencies of a and x gives
9
10
Math ReviewUp to this point the trigonometry utilized in 207 involved the basic sine and cosine function definitions applied to fixed triangles.
Review of graphs of sine and cosine functions
11
range
amplitude=a
period =
12
A buoy oscillates up and down as waves go past. The buoy moves a total of 4.0 feet from its low point to its high point, and then returns to its high point every 6 seconds.
Write an equation that gives the buoys vertical position y at time t if the buoy is at its highest point when t =0.
13
x=0x=A
x=A
14
A = amplitude, the largest displacement from equilibrium
period
frequency
15
x=0x=A
x=A
The force needed to stretch a spring an amount x is F = kx.
Therefore, the work done in stretching the spring is
Area of a triangle with sides kx and x
16