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Chapter 12
Vibrations and Waves
Periodic Motion
Any repeated motion
Examples?
Describe velocity, force and
acceleration at a, b and c
a
c
b
c is the equilibrium or rest position
The force is called the restoring force
Any periodic motion where the
restoring force is proportional to the
displacement is called simple
harmonic motion
Frestore = -kDx
Hooke’s Law
Felastic = -kx
spring force
- because
force is
opposite
displacement
spring constant: how
stiff the spring is
x = displacement
from rest position
I have a mass of 85 kg. I jump on a
trampoline and it compresses 40 cm before
propelling me up. What is the spring constant
of the trampoline?
Felastic = Fweight
Fweight = mg
Fweight = 834 N
x = 0.40 m
k = -F/-x = 2085 N/m
A pendulum moves in simple harmonic
motion when displacement angles are
small, less than 15°
Forces on a Pendulum
Net Force?
acceleration?
velocity?
Net Force?
acceleration?
velocity?
FT
FT
Fgy
mg
Fgx
mg
Time Measurements
Period, T, is the time for one
back and forth motion in
seconds
Frequency, f, is how often
back and forth motions occur
in 1 second, measured in
hertz, Hz
1
f 
T
1
1 Hz 
sec
Period of a Pendulum
L
T  2
g
Period only depends on L,
the length of the pendulum
Period of a mass-spring system
m
T  2
k