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Figure \(\PageIndex{3}\): A graph of the kinetic energy (red), potential energy (blue), and total energy (green) of a simple harmonic oscillator. The force is equal to F = − \(\frac{dU}{dx}\). The equilibrium position is shown as a black dot and is the point where the force is equal to zero.
- 15.2: Simple Harmonic Motion
List the characteristics of simple harmonic motion; Explain...
- 15.2: Simple Harmonic Motion
List the characteristics of simple harmonic motion; Explain the concept of phase shift; Write the equations of motion for the system of a mass and spring undergoing simple harmonic motion; Describe the motion of a mass oscillating on a vertical spring
A simple harmonic oscillator is a mass on the end of a spring that is free to stretch and compress. The motion is oscillatory and the math is relatively simple.
In these notes, we introduce simple harmonic oscillator motions, its defining equation of motion, and the corresponding general solutions. We discuss how the equation of motion of the pendulum approximates the simple harmonic oscillator equation of motion in the small angle approximation.
List the characteristics of simple harmonic motion; Explain the concept of phase shift; Write the equations of motion for the system of a mass and spring undergoing simple harmonic motion; Describe the motion of a mass oscillating on a vertical spring
1. One of the most important examples of periodic motion is simple harmonic motion (SHM), in which some physical quantity varies sinusoidally. Suppose a function of time has the form of a sine wave function, y(t) = Asin(2πt / T ) (23.1.1) where A > 0 is the amplitude (maximum value).
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
