Transcript Vibrations and Waves

Vibrations and Waves
Hooke’s Law
Elastic Potential Energy
Simple Harmonic Motion
Springs
• _________ force of spring
pushes/pulls mass toward
___________
Fs  kx
13.1
• Results in simple _______
motion
• Newton’s 2nd Law gives
harmonic _______ equation
k
a x
m
13.2
Fig. 13.1, p. 426
Describing SHM
• Amplitude, A, is _________ displacement
from ________. Object oscillates between
x = +A and x = −A
• Period, T, is the time required to move
through one complete ______
• Frequency, f, is the number of complete
cycles per unit _____. f = 1/T
Elastic Potential Energy
• Recall energy ______
in spring
PEs  kx
1
2
2
13.3
• Apply _____-_______
theorem
Wnc  KE  PE
Fig. 13.4, p. 429
Velocity as a Function of Position
• Energy at maximum
___________ equals
energy at ___ point in
cycle
1
2
kA  mv  kx
2
1
2

2
k 2
2
v
A x
m
1
2
2
 13.6
Fig. 13.7, p. 431
SHM and Uniform Circular Motion
• The projection of a
ball rotating with
constant angular
speed, , on a two
dimensional surface
moves with simple
harmonic motion
2 A
2 A
v0 
T 
T
v0
Figs. 13.8 & 13.9, p. 433
SHM and Uniform Circular Motion
• Equate energy at
maximum __________
to energy at _________
position
• Substitute into
expression for period
m
T  2
k
1
2
kA  mv
2
1
2
2
0
A
m

v0
k
k
13.8   2 f 
m
13.11