Review Exam 1

Simple Harmonic Motion

11-1 Simple Harmonic MotionThe force exerted by the spring depends on the displacement:

(11-1)

11-2 Energy in the Simple Harmonic Oscillator

We already know that the potential energy of a spring is given by:

The total mechanical energy is then:

(11-3)

The total mechanical energy will be conserved, as we are assuming the system is frictionless.

11-2 Energy in the Simple Harmonic Oscillator

The total energy is

And we can write:

(11-4c)

This can be solved for the velocity as a function of position:

(11-5)

where

11-3 The Period and Sinusoidal Nature of SHM

(11-7a)

(11-7b)

11-4 The Simple Pendulum

Therefore, for small angles, we have:

where

The period and frequency are:

(11-11a)

(11-11b)

Harmonic Disturbance

11-7 Wave Motion

Wave characteristics:

• Amplitude, A

• Wavelength, λ

• Frequency f and period T

• Wave velocity (11-12)

Waves on a String

lengthmass where

F

v

nd1,2,3,...an where

n2L

vf;

n

2Lλ

T

nn

Guitar String

Why?

λ(sound)λ(string)but f(sound)f(string)

nd1,2,3,...an where

f n 2L

vf SOUNDSTRING

1,2,3,...nfor n 2L

vf and

n

2Lλ sound

nn

1,3,5,...nfor n 4L

vf and

n

4Lλ sound

nn

Loud

Quiet

http://library.thinkquest.org/19537/cgi-bin/showharm.cgi#

Both Source and Observer Moving

sourcesound

observersound

sound

source

sound

observer

'

v v

v v f

vv

1

vv

1

f f

Exam• 5 problems • 3 Qualitative (30 points)• 2 Quantitative (70 points)• Suggestions– Read problem carefully– Underline important stuff, cross out extraneous stuff– Outline solution if out of time– If you think you need a quantity that doesn’t appear to

you to be there, make one up.– Study Equation Sheet.