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Questions and Answers
Which equation describes the displacement in simple harmonic motion?
Which equation describes the displacement in simple harmonic motion?
What is the relationship between angular frequency (ω) and frequency (f) in SHM?
What is the relationship between angular frequency (ω) and frequency (f) in SHM?
Which type of simple harmonic motion involves an external force that maintains the motion?
Which type of simple harmonic motion involves an external force that maintains the motion?
What happens to the amplitude in damped simple harmonic motion over time?
What happens to the amplitude in damped simple harmonic motion over time?
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What concept explains the conversion between kinetic and potential energy in SHM?
What concept explains the conversion between kinetic and potential energy in SHM?
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Which parameter in the displacement equation determines the initial displacement and velocity?
Which parameter in the displacement equation determines the initial displacement and velocity?
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What is a classic example of SHM due to gravitational force?
What is a classic example of SHM due to gravitational force?
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What does the velocity equation v(t) = -Aω sin(ωt + φ) describe?
What does the velocity equation v(t) = -Aω sin(ωt + φ) describe?
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In what type of SHM does no external force apply and motion is only due to the restoring force?
In what type of SHM does no external force apply and motion is only due to the restoring force?
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What occurs when the frequency of an external force matches the natural frequency of a system in SHM?
What occurs when the frequency of an external force matches the natural frequency of a system in SHM?
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Study Notes
Simple Harmonic Motion (SHM)
Definition: Simple harmonic motion is a type of oscillatory motion where the acceleration of the object is directly proportional to its displacement from its equilibrium position.
Key Characteristics:
- Periodic motion: The object moves back and forth repeatedly, covering the same distance in a fixed time.
- Constant amplitude: The maximum displacement from the equilibrium position remains constant.
- Constant frequency: The number of oscillations per second remains constant.
Mathematical Representation:
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Displacement equation: x(t) = A cos(ωt + φ)
- x: displacement from equilibrium position
- A: amplitude (maximum displacement)
- ω: angular frequency (related to frequency by ω = 2πf)
- t: time
- φ: phase angle (initial displacement)
- Velocity equation: v(t) = -Aω sin(ωt + φ)
- Acceleration equation: a(t) = -Aω² cos(ωt + φ)
Types of SHM:
- Free SHM: No external force is applied, and the motion is solely due to the restoring force.
- Damped SHM: An external force, such as friction, opposes the motion, causing the amplitude to decrease over time.
- Forced SHM: An external force, such as a driving force, is applied to maintain the motion.
Real-World Applications:
- Pendulums: A classic example of SHM, where the pendulum's motion is due to the gravitational force.
- Springs: When a spring is stretched or compressed, it exhibits SHM.
- Vibrations: Many mechanical systems, such as engines and bridges, exhibit SHM due to the forces acting upon them.
Important Concepts:
- Energy conversion: In SHM, energy is converted between kinetic energy (during motion) and potential energy (at the extremes of displacement).
- Phase and phase shift: The phase angle φ determines the initial displacement and velocity of the object.
- Resonance: When the frequency of an external force matches the natural frequency of the system, SHM occurs with maximum amplitude.
Simple Harmonic Motion (SHM)
Definition and Characteristics
- Simple harmonic motion is a type of oscillatory motion where the acceleration of the object is directly proportional to its displacement from its equilibrium position.
- It is a periodic motion, meaning the object moves back and forth repeatedly, covering the same distance in a fixed time.
- The amplitude (maximum displacement) and frequency (number of oscillations per second) remain constant.
Mathematical Representation
- Displacement equation: x(t) = A cos(ωt + φ), where x is the displacement from the equilibrium position, A is the amplitude, ω is the angular frequency, t is time, and φ is the phase angle.
- Velocity equation: v(t) = -Aω sin(ωt + φ).
- Acceleration equation: a(t) = -Aω² cos(ωt + φ).
Types of SHM
- Free SHM: No external force is applied, and the motion is solely due to the restoring force.
- Damped SHM: An external force, such as friction, opposes the motion, causing the amplitude to decrease over time.
- Forced SHM: An external force, such as a driving force, is applied to maintain the motion.
Real-World Applications
- Pendulums exhibit SHM due to the gravitational force.
- Springs exhibit SHM when stretched or compressed.
- Many mechanical systems, such as engines and bridges, exhibit SHM due to the forces acting upon them.
Important Concepts
- Energy conversion: In SHM, energy is converted between kinetic energy (during motion) and potential energy (at the extremes of displacement).
- Phase and phase shift: The phase angle φ determines the initial displacement and velocity of the object.
- Resonance: When the frequency of an external force matches the natural frequency of the system, SHM occurs with maximum amplitude.
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Description
Test your knowledge of Simple Harmonic Motion, a type of oscillatory motion where acceleration is proportional to displacement from equilibrium position. Key characteristics include periodic motion, constant amplitude, and constant frequency.
