Announcements
1. HW10 due April 15
Announcements
4. Final exam:
April 25, Saturday, 10 am to noon
2. Midterm2:
if you want to look at your scantron, see Prof. Reitze
before end of today
If you forgot to bring ID during exam, you must see
Prof. Reitze with your ID or your exam will not be graded.
3. Make-up exam:
April 22 Wednesday, 7:20 – 9:10 pm, meet at Prof. Reitze’s
office (NPB 2265)
covers all material in the course.
To take the make-up exam, you must obtain permission
from Prof. Chan or Prof. Reitze.
Room assignments:
last name
room
A-GAR
computer science engineering A101
GEE-J
Fine Arts B 105
K-MAZ
Florida Gym 230
MCC-O
Florida Gym 260
P-R
Florida Gym 280
S-Z
Williamson 100
roughly ½ of questions on topics covered in midterms,
the rest on Chapters 9, 13, 14
13. Vibrations and Waves
Found everywhere in the universe and in daily life.
• hearing and vision.
• Ultrasound diagnostics.
Vibrations and Waves
Hooke’s law
F = -kx
1.Force is proportional to
displacement from equilibrium
position
2. Force always opposes x
Image: Absorption, Transmission,
and Reflection of ultrasound
F = -kx
1.Force always
points towards
the equilibrium
position
2.It is called the
restoring
force.
Simple harmonic motion
• Amplitude, A
– The amplitude is the maximum position of
the object relative to the equilibrium
position
– In the absence of friction, an object in
simple harmonic motion will oscillate
between the positions x = ±A
Simple harmonic motion
1
Time period T and frequency f
Energy keeps going back and forth
between kinetic and potential.
At x = A,
• The period, T, is the time that it takes for the
object to complete one complete cycle of
motion
K.E = 0
P.E = ½ K A2
• From x = A to x = - A and back to x = A
• The frequency, ƒ, is the number of complete
cycles or vibrations per unit time
At x = 0,
P.E. = 0
• ƒ=1/T
• Frequency is the reciprocal of the period
• Units are cycles per second (s-1) or hertz (Hz)
K.E. = ½ mv2
F = -kx
• Conservation of Energy allows a calculation
of the velocity of the object at any position in
its motion
k
v =±
A2 − x 2
m
(
)
The ± indicates the object can
be traveling in either direction
F = ma
v =±
k
A2 − x 2
m
(
)
X = ±A
X=0
Magnitude of
velocity
Magnitude of
acceleration
KE
0
Max
Max
0
0
Max
PE
Max
0
Can we use kinematic equations?
v = v o + at
NO
∆x = v o t +
1 2
at
2
v 2 = v o2 + 2 a∆ x
Oscillates vertically-Becomes wave in time
2
90-θ
vt
θ
Simple Harmonic motion
x = A cos ωt
two important parameters: A and ω
•
•
•
•
•
x = A cos ωt
v = -A ω sin ωt
a = -Aω2 cos ωt
2πf = ω
ω=
F = -kx = ma
k
v =±
A2 − x 2
m
(
k
m
1
f =
2π
)
Simple
Harmonic
Motion
(SHM)
v = -A ω sin ωt
a = -Aω2 cos ωt
k
m
T = 2π
m
k
• the uniformly accelerated motion
equations cannot be used
3
Simple Pendulum
• The simple
pendulum is another
example of simple
harmonic motion
• The force is the
component of the
weight tangent to
the path of motion
Ft = - m g sin θ
≈ -mg θ (for small θ)
= -mg (s/L)
T = 2π
L
g
T = 2π
L
g
4