Textbook Question
When a guitar string plays the note 'A,' the string vibrates at 440 Hz. What is the period of the vibration?
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Ch 15: Oscillations
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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Table of contents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics33
- Ch 34: Ray Optics57
- Ch 36: Special Relativity38
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
Chapter 15, Problem 7c
FIGURE EX15.7 is the position-versus-time graph of a particle in simple harmonic motion. What is vmax?
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Identify the amplitude (A) of the motion from the graph. The amplitude is the maximum displacement from the equilibrium position. From the graph, the amplitude is 4 cm.
Determine the period (T) of the motion. The period is the time it takes for one complete cycle of motion. From the graph, the particle completes one cycle from t = 0 to t = 4 s, so T = 4 s.
Calculate the angular frequency (ω) using the formula: ω = 2π / T. Substitute the value of T = 4 s into the formula to find ω.
Use the formula for maximum velocity in simple harmonic motion: vₘₐₓ = Aω. Substitute the values of A (4 cm) and ω (calculated in the previous step) into this formula.
Ensure the units are consistent. If needed, convert the amplitude from cm to meters before calculating vₘₐₓ. The final expression for vₘₐₓ will be in meters per second (m/s).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Simple Harmonic Motion (SHM)
Simple Harmonic Motion is a type of periodic motion where an object oscillates around an equilibrium position. The motion is characterized by a restoring force proportional to the displacement from the equilibrium, leading to sinusoidal position, velocity, and acceleration graphs. In SHM, the maximum displacement from the equilibrium is known as the amplitude.
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Simple Harmonic Motion of Pendulums
Velocity in SHM
In Simple Harmonic Motion, the velocity of the oscillating object varies sinusoidally with time. The maximum velocity, denoted as vₘₐₓ, occurs as the object passes through the equilibrium position. It can be calculated using the formula vₘₐₓ = ωA, where ω is the angular frequency and A is the amplitude of the motion.
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Position-Time Graph
A position-time graph visually represents the position of an object as a function of time. In the context of SHM, this graph typically shows a sinusoidal wave, indicating periodic motion. The slope of the graph at any point gives the instantaneous velocity, and the maximum slope corresponds to the maximum velocity of the particle.
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Related Practice
Textbook Question
What are the (a) amplitude, (b) frequency, and (c) phase constant of the oscillation shown in FIGURE EX15.6?
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Textbook Question
FIGURE EX15.7 is the position-versus-time graph of a particle in simple harmonic motion. What is the phase constant?
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Textbook Question
An object in simple harmonic motion has an amplitude of 8.0 cm, n angular frequency of 0.25 rad/s, and a phase constant of π rad. Draw a velocity graph showing two cycles of the motion.
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Textbook Question
An air-track glider attached to a spring oscillates with a period of 1.5 s. At t = 0 s the glider is 5.00 cm left of the equilibrium position and moving to the right at 36.3 cm/s. What is the phase constant?
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Textbook Question
A 200 g air-track glider is attached to a spring. The glider is pushed in 10 cm and released. A student with a stopwatch finds that 10 oscillations take 12.0 s. What is the spring constant?
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