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Questions and Answers
What is the defining characteristic of simple harmonic motion?
What is the defining characteristic of simple harmonic motion?
What is the term for the maximum displacement from the equilibrium position in SHM?
What is the term for the maximum displacement from the equilibrium position in SHM?
What is the unit of frequency in SHM?
What is the unit of frequency in SHM?
What is the relationship between kinetic energy and potential energy in SHM?
What is the relationship between kinetic energy and potential energy in SHM?
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Which of the following is an example of SHM?
Which of the following is an example of SHM?
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What is the phase angle in the displacement equation of SHM?
What is the phase angle in the displacement equation of SHM?
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What is the effect of resonance on a system?
What is the effect of resonance on a system?
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What is the purpose of damping in a system?
What is the purpose of damping in a system?
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What happens to the amplitude of a system when it is in resonance?
What happens to the amplitude of a system when it is in resonance?
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What is the difference between damping and resonance?
What is the difference between damping and resonance?
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What happens to the energy of a system when it is damped?
What happens to the energy of a system when it is damped?
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Study Notes
Simple Harmonic Motion (SHM)
Definition
- Simple harmonic motion is a type of periodic motion where the restoring force is proportional to the displacement from the equilibrium position.
- The motion is sinusoidal and repeats at regular intervals.
Characteristics
- Displacement: The distance from the equilibrium position.
- Amplitude: The maximum displacement from the equilibrium position.
- Period: The time taken to complete one cycle of motion.
- Frequency: The number of cycles per second, measured in Hz (1/s).
- Phase: The initial angle of the motion.
Equations of Motion
-
Displacement equation: x(t) = A cos(ωt + φ)
- x(t) = displacement at time t
- A = amplitude
- ω = angular frequency (2πf)
- φ = phase angle
- Velocity equation: v(t) = -Aω sin(ωt + φ)
- Acceleration equation: a(t) = -Aω^2 cos(ωt + φ)
Energy in SHM
- Kinetic energy: maximum at the equilibrium position, minimum at the amplitude
- Potential energy: maximum at the amplitude, minimum at the equilibrium position
- Total energy: constant, converted between kinetic and potential energy
Examples
- Mass on a spring
- Pendulum
- Vibrating string
- Electric circuits with capacitors and inductors
Simple Harmonic Motion (SHM)
- SHM is a type of periodic motion where the restoring force is proportional to the displacement from the equilibrium position and the motion is sinusoidal.
Characteristics of SHM
- Displacement is the distance from the equilibrium position.
- Amplitude is the maximum displacement from the equilibrium position.
- Period is the time taken to complete one cycle of motion.
- Frequency is the number of cycles per second, measured in Hz (1/s).
- Phase is the initial angle of the motion.
Equations of SHM
- The displacement equation is x(t) = A cos(ωt + φ), where x(t) is the displacement at time t, A is the amplitude, ω is the angular frequency, and φ is the phase angle.
- The velocity equation is v(t) = -Aω sin(ωt + φ).
- The acceleration equation is a(t) = -Aω^2 cos(ωt + φ).
Energy in SHM
- Kinetic energy is maximum at the equilibrium position and minimum at the amplitude.
- Potential energy is maximum at the amplitude and minimum at the equilibrium position.
- Total energy is constant and is converted between kinetic and potential energy.
Examples of SHM
- A mass on a spring exhibits SHM.
- A pendulum shows SHM.
- A vibrating string demonstrates SHM.
- Electric circuits with capacitors and inductors can also exhibit SHM.
Simple Harmonic Motion (SHM)
Definition
- SHM is a type of periodic motion where the restoring force is proportional to the displacement from the equilibrium position.
- The motion is sinusoidal and repeats at regular intervals.
Characteristics
- Displacement is the distance from the equilibrium position.
- Amplitude is the maximum displacement from the equilibrium position.
- Period is the time taken to complete one cycle of motion.
- Frequency is the number of cycles per second, measured in Hz (1/s).
- Phase is the initial angle of the motion.
Equations of Motion
- Displacement equation: x(t) = A cos(ωt + φ), where x(t) is displacement at time t, A is amplitude, ω is angular frequency (2πf), and φ is phase angle.
- Velocity equation: v(t) = -Aω sin(ωt + φ).
- Acceleration equation: a(t) = -Aω^2 cos(ωt + φ).
Energy in SHM
- Kinetic energy is maximum at the equilibrium position and minimum at the amplitude.
- Potential energy is maximum at the amplitude and minimum at the equilibrium position.
- Total energy is constant and converted between kinetic and potential energy.
Examples of SHM
- Mass on a spring.
- Pendulum.
- Vibrating string.
- Electric circuits with capacitors and inductors.
Important Concepts
- Resonance and damping are important concepts in SHM.
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Description
Learn about simple harmonic motion, its definition, and characteristics including displacement, amplitude, period, and frequency. Understand the concept of periodic motion and its applications.
