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- Period and Frequency in Oscillations. In the absence of friction, the time to complete one oscillation remains constant and is called the period (T). Its units are usually seconds, but may be any convenient unit of time.
- Characteristics of Simple Harmonic Motion. A very common type of periodic motion is called simple harmonic motion (SHM). A system that oscillates with SHM is called a simple harmonic oscillator.
- Equations of SHM. Consider a block attached to a spring on a frictionless table (Figure 15.4). The equilibrium position (the position where the spring is neither stretched nor compressed) is marked as x=0x=0.
- Summary of Equations of Motion for SHM. In summary, the oscillatory motion of a block on a spring can be modeled with the following equations of motion
- Period and Frequency in Oscillations. In the absence of friction, the time to complete one oscillation remains constant and is called the period (T). Its units are usually seconds, but may be any convenient unit of time.
- Characteristics of Simple Harmonic Motion. A very common type of periodic motion is called simple harmonic motion (SHM). A system that oscillates with SHM is called a simple harmonic oscillator.
- Equations of SHM. Consider a block attached to a spring on a frictionless table (Figure \(\PageIndex{3}\)). The equilibrium position (the position where the spring is neither stretched nor compressed) is marked as x = 0 .
- Summary of Equations of Motion for SHM. In summary, the oscillatory motion of a block on a spring can be modeled with the following equations of motion
Simple harmonic motion can serve as a mathematical model for a variety of motions, but is typified by the oscillation of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's law. The motion is sinusoidal in time and demonstrates a single resonant frequency.
A particularly important kind of oscillatory motion is called simple harmonic motion. This is what happens when the restoring force is linear in the displacement from the equilibrium position: that is to say, in one dimension, if \(x_0\) is the equilibrium position, the restoring force has the form
Describe Hooke’s law and Simple Harmonic Motion; Describe periodic motion, oscillations, amplitude, frequency, and period; Solve problems in simple harmonic motion involving springs and pendulums
Simple Harmonic Motion. Simple harmonic motion is typified by the motion of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's Law. The motion is sinusoidal in time and demonstrates a single resonant frequency. Motion equations. Motion calculation.
Key terms. Equations. Force, displacement, velocity, and acceleration for an oscillator. Simple harmonic motion is governed by a restorative force. For a spring-mass system, such as a block attached to a spring, the spring force is responsible for the oscillation (see Figure 1). F s = − k x.
