Chapter 13
Oscillations About Equilibrium
(Cont.)
Dr. Jie Zou PHY 1151G
Department of Physics
1
Outline
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Energy conservation in oscillatory
motion
The simple pendulum
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
The period of a simple pendulum
Driven oscillations and resonance
Dr. Jie Zou PHY 1151G
Department of Physics
2
Energy conservation in
oscillatory motion
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
In an ideal system with no friction or other
nonconservative forces, the total energy (E)
is conserved.
For a mass on a horizontal spring:
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Total energy E = K + U
K = kinetic energy = (1/2)mv2
U = elastic potential energy = (1/2)kx2
The kinetic (K) and potential (U) energy change with time,
but the total energy E is conserved.
It can be shown that E = (1/2)kA2, where A is the amplitude
of oscillation.
Dr. Jie Zou PHY 1151G
Department of Physics
3
Energy vs. position in simple
harmonic motion
Dr. Jie Zou PHY 1151G
Department of Physics
4
Example

A 0.980-kg block slides on a
frictionless, horizontal surface
with a speed of 1.32 m/s. The
block encounters an
unstretched spring with a force
constant of 245 N/m.
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(a) How far is the spring compressed
before the block comes to rest?
(b) How long is the block in contact with
the spring before it comes to rest?
Answers: (a) 0.0835 m (b) 0.0993 s
Dr. Jie Zou PHY 1151G
Department of Physics
5
The pendulum
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
L

m
Simple pendulum: consists of a
mass m suspended by a light
string or rod of length L.
L
Period of a pendulum: T  2
g
The period of a simple pendulum
depends on the length of the
pendulum and the acceleration of
gravity. It is independent of the
mass and the amplitude.
Dr. Jie Zou PHY 1151G
Department of Physics
6
Example
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
A pendulum is constructed from a
string 0.627 m long attached to a
mass of 0.250 kg. The pendulum
completes one oscillation every
1.59 s. Find the acceleration of
gravity, g.
“Gravity maps” are valuable tools
for geologists attempting to
understand the underground
properties of a given region, such
as density of rocks.
Dr. Jie Zou PHY 1151G
Department of Physics
7
Driven oscillations and
resonance
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Natural frequency, f0: The
frequency at which the
system oscillates when it is
not driven.
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In general, driving any system
at a frequency near its natural
frequency results in large
oscillations.
Resonance: This type of
large response, due to
Tacoma Narrows bridge,
frequency matching, is
1940
known as resonance.
Dr. Jie Zou PHY 1151G

Department of Physics
8
Homework

See online homework on
www.masteringphysics.com
Dr. Jie Zou PHY 1151G
Department of Physics
9