A simple harmonic oscillator is a system where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement. It exhibits periodic motion characterized by sinusoidal oscillations.
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The equation of motion for a simple harmonic oscillator is $F = -kx$, where $k$ is the spring constant and $x$ is the displacement.
The angular frequency $\omega$ of a simple harmonic oscillator is given by $\omega = \sqrt{\frac{k}{m}}$, where $m$ is the mass of the object.
The period $T$ of a simple harmonic oscillator, which is the time for one complete cycle, is given by $T = 2\pi \sqrt{\frac{m}{k}}$.
In simple harmonic motion, kinetic energy and potential energy are exchanged but their sum remains constant, indicating conservation of mechanical energy.
The maximum speed of an object in simple harmonic motion occurs as it passes through its equilibrium position.
Review Questions
What is the relationship between force and displacement in a simple harmonic oscillator?
How do you calculate the period of a simple harmonic oscillator?
In terms of energy, what happens during one cycle of simple harmonic motion?