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.

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x=0x=A

x=A

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A = amplitude, the largest displacement from equilibrium

period

frequency

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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

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