Disclaimer--please double check ALL formulas with the textbook,as there may be formatting issues with equations on the webpagethat could lead to confusion.
SUMMARY
13.1 Hooke’s Law
Simple harmonic motion occurs when the net force on an
object along the direction of motion is proportional to the
object’s displacement and in the opposite direction:
Fs = --kx [13.1]
This is called Hooke’s law.
The time required for one complete
vibration is called the period of the motion. The reciprocal
of the period is the frequency of the motion,
which is the number of oscillations per second.
When an object moves with simple harmonic motion, its
acceleration as a function of position is
a = --k/m x [13.2]
13.2 Elastic Potential Energy
The energy stored in a stretched or compressed spring or in
some other elastic material is called elastic potential energy:
PE = 1/2 kx2[13.3]
The velocity of an object as a function of position, when
the object is moving with simple harmonic motion, is
v = +/- √k/m (A2 - x2) [13.6]
13.4 Position, Velocity, and Acceleration as a Function of Time
The period of an object of mass m moving with simple harmonic
motion while attached to a spring of spring constant k is
T = 2 π √m/k [13.8]
where T is independent of the amplitude A.
The frequency of an object–spring system is f = 1/T.
The angular frequency ω of the system in rad/s is
ω = 2 π f = √k/m [13.11]
When an object is moving with simple harmonic motion,
the position, velocity, and acceleration of the object as a function of time are given by
x = A cos (2 π f t) [13.14a]
v = --A ω sin (2 π f t) [13.14b]
a = --A ω2 cos (2 π f t) [13.14c]
13.5 Motion of a Pendulum
A simple pendulum of length L moves with simple harmonic
motion for small angular displacements from the
vertical, with a period of
T = 2П √L / g [13.15]
13.7 Waves
In a transverse wave the elements of the medium move in a
direction perpendicular to the direction of the wave. An
example is a wave on a stretched string.
In a longitudinal wave the elements of the medium
move parallel to the direction of the wave velocity. An example
is a sound wave.
13.8 Frequency, Amplitude, and Wavelength
The relationship of the speed, wavelength, and frequency
of a wave is
v = f λ [13.17]
This relationship holds for a wide variety of different waves.
13.9 The Speed of Waves on Strings
The speed of a wave traveling on a stretched string of mass
per unit length and under tension F is
v = √F/u [13.18]
13.10 Interference of Waves
The superposition principle states that if two or more
traveling waves are moving through a medium, the resultant
wave is found by adding the individual waves together
point by point. When waves meet crest to crest and
trough to trough, they undergo constructive interference.
When crest meets trough, the waves undergo destructive
interference.
13.11 Reflection of Waves
When a wave pulse reflects from a rigid boundary, the
pulse is inverted. When the boundary is free, the reflected
pulse is not inverted.
AP Physics Vibrations and Waves Power Point--Serway
ANSWERS
to Quick Quizzes and Even Numbered Questions and Problems from the text.
Also SOLUTIONS to problems!
NOTICE:
Disclaimer--please double check ALL formulas with the textbook, as there may be formatting issues with equations on the webpage that could lead to confusion.
SUMMARY
13.1 Hooke’s Law
Simple harmonic motion occurs when the net force on an
object along the direction of motion is proportional to the
object’s displacement and in the opposite direction:
Fs = --kx [13.1]
This is called Hooke’s law.The time required for one complete
vibration is called the period of the motion. The reciprocal
of the period is the frequency of the motion,
which is the number of oscillations per second.
When an object moves with simple harmonic motion, its
acceleration as a function of position is
a = --k/m x [13.2]
13.2 Elastic Potential Energy
The energy stored in a stretched or compressed spring or in
some other elastic material is called elastic potential energy:
PE = 1/2 kx2 [13.3]
The velocity of an object as a function of position, when
the object is moving with simple harmonic motion, is
v = +/- √k/m (A2 - x2) [13.6]
13.4 Position, Velocity, and Acceleration as a Function of Time
The period of an object of mass m moving with simple harmonic
motion while attached to a spring of spring constant k is
T = 2 π √m/k [13.8]
where T is independent of the amplitude A.The frequency of an object–spring system is f = 1/T.
The angular frequency ω of the system in rad/s is
ω = 2 π f = √k/m [13.11]
When an object is moving with simple harmonic motion,
the position, velocity, and acceleration of the object as a
function of time are given by
x = A cos (2 π f t) [13.14a]
v = --A ω sin (2 π f t) [13.14b]
a = --A ω2 cos (2 π f t) [13.14c]
13.5 Motion of a Pendulum
A simple pendulum of length L moves with simple harmonic
motion for small angular displacements from the
vertical, with a period of
T = 2П √L / g [13.15]
13.7 Waves
In a transverse wave the elements of the medium move in a
direction perpendicular to the direction of the wave. An
example is a wave on a stretched string.
In a longitudinal wave the elements of the medium
move parallel to the direction of the wave velocity. An example
is a sound wave.
13.8 Frequency, Amplitude, and Wavelength
The relationship of the speed, wavelength, and frequency
of a wave is
v = f λ [13.17]
This relationship holds for a wide variety of different waves.13.9 The Speed of Waves on Strings
The speed of a wave traveling on a stretched string of mass
per unit length and under tension F is
v = √F/u [13.18]
13.10 Interference of Waves
The superposition principle states that if two or more
traveling waves are moving through a medium, the resultant
wave is found by adding the individual waves together
point by point. When waves meet crest to crest and
trough to trough, they undergo constructive interference.
When crest meets trough, the waves undergo destructive
interference.
13.11 Reflection of Waves
When a wave pulse reflects from a rigid boundary, the
pulse is inverted. When the boundary is free, the reflected
pulse is not inverted.