Chapter 13
Oscillations About Equilibrium
03/28/05
Dr. Jie Zou PHY 1151G
Department of Physics
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Outline
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Oscillations
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Periodic motions
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Basic cause for oscillations
Period and frequency
Simple harmonic motions
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Classical example: A mass attached to a spring
Position as a function of time for a simple
harmonic motion
Period of a mass on a spring
Dr. Jie Zou PHY 1151G
Department of Physics
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Oscillations
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03/28/05
Oscillations: When systems are
displaced from equilibrium, it often
results in oscillations back and
forth from one side of the
equilibrium position to the other.
Basic cause of oscillations:
When an object is displaced from a
position of stable equilibrium it
experiences a restoring force that
is directed back toward the
equilibrium position.
Dr. Jie Zou PHY 1151G
Department of Physics
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Periodic Motion
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Periodic motion: A motion that
repeats itself over and over is
referred to as periodic motion.
Definition of period, T : time
required for one cycle (one oscillation)
of a periodic motion.
The trace of an
n SI unit: second or s.
electrocardiogram
n Definition of frequency, f : the
(ECG or EKG).
number of oscillations per unit of time.
f = 1/T.
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03/28/05
SI unit: per second = 1/s = Hz.
Dr. Jie Zou PHY 1151G
Department of Physics
4
Example: Periodic motion
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If the processing speed of a personal
computer is 1.80 GHz, how much time is
required for one processing cycle?
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A tennis ball is hit back and forth between two
players warming up for a match. If it takes
2.31 s for the ball to go from one player to the
other, what are the period and frequency of
the tennis ball’s motion?
03/28/05
Dr. Jie Zou PHY 1151G
Department of Physics
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Simple harmonic motion
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A classical example of
simple harmonic motion:
The mass-spring system.
Key feature of a massspring system: A spring
exerts a restoring force that is
proportional to the
displacement from equilibrium,
F = - kx.
Dr. Jie Zou PHY 1151G
Department of Physics
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Position versus time for simple
harmonic motion
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Position versus time in simple
harmonic motion: x = Acos 2π t
T 
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Here we suppose that the cart is
released at t = 0 from rest at x = A .
Amplitude, A : it represents the
maximum displacement of the cart
on either side of equilibrium.
Period, T : the cart’s motion
repeats with a period T.
Dr. Jie Zou PHY 1151G
Department of Physics
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Example 13-1
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An air-track cart attached to a spring
completes one oscillation every 2.4 s. At t = 0
the cart is released from rest at a distance of
0.10 m from its equilibrium position. What is
the position of the cart at (a) 0.30 s, (b) 0.60 s,
(c) 2.7 s, and (d) 3.0 s?
03/28/05
Dr. Jie Zou PHY 1151G
Department of Physics
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Period of a mass on a spring
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A horizontal spring: T = 2π
k
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equilibrium position.
Here m is the mass (kg), and
k is the force constant of the
spring (N/m), and T is the
period (s).
The period, T, increases with
the mass and decreases with
the spring’s force constant.
The period, T, is independent
of the amplitude, A .
Dr. Jie Zou PHY 1151G
Department of Physics
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A vertical spring
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A vertical spring is in
equilibrium at y=-y0.
At this equilibrium position, the
spring stretches by an amount
y0 given by
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03/28/05
ky0 = mg or y0 = mg/k
A mass on a vertical spring
oscillates about the equilibrium
point y = -y0.
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The period is also T = 2π
Dr. Jie Zou PHY 1151G
Department of Physics
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Active-Example 13-2
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03/28/05
When a 0.420-kg mass is attached to a
spring, it oscillates with a period of 0.350
s. If, instead, a different mass, m2, is
attached to the same spring, it oscillates
with a period of 0.700 s. Find (a) the
force constant of the spring and (b) the
mass m2.
Real world physics: the relationship
between the mass and period is used by
NASA to measure the mass of
astronauts in orbit - The Body Mass
Measurement Device (BMMD)
Dr. Jie Zou PHY 1151G
Department of Physics
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Homework #11 (03/28/05)
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Chapter 13, Page 413, Problems: # 6, 8,
14, 27, 29.
03/28/05
Dr. Jie Zou PHY 1151G
Department of Physics
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