# Harmonic Oscillator- Is this correct?

• kubaanglin
In summary, a harmonic oscillator is a physical system that exhibits simple harmonic motion, described by a sine or cosine function. It works by having a restoring force that is proportional to the displacement from its equilibrium position. Examples of harmonic oscillators include a simple pendulum, mass-spring systems, and vibrating guitar strings. The equation for a harmonic oscillator is F = -kx, where F is the restoring force, k is the spring constant, and x is the displacement. This is also known as Hooke's law. A harmonic oscillator differs from a non-harmonic oscillator in that it follows a sinusoidal pattern of motion, while a non-harmonic oscillator has a more complex motion pattern due to its restoring force not following a simple
kubaanglin

## Homework Statement

[/B]
What is the shortest time required for a harmonic oscillator to move from ##x = A## to ##x = \frac{A}{2}##? Express your answer in terms of the period ##T##.

## Homework Equations

[/B]
##x(t)=Acos(\omega t)=Acos(2\pi\frac{t}{T})##

## The Attempt at a Solution

##A=Acos(0)## which means ##\frac{t}{T}=## whole number
##\frac{A}{2}=Acos(\frac{\pi}{3})## which means ##\frac{t}{T}=\frac{1}{6}##
##t=\frac{T}{6}##

Very good. It looks correct to me.

## 1. What is a harmonic oscillator?

A harmonic oscillator is a physical system that has a repeating pattern of motion, which is described by a mathematical function called a sine or cosine function. This type of motion is known as simple harmonic motion.

## 2. How does a harmonic oscillator work?

A harmonic oscillator works by having a restoring force that pulls it back to its equilibrium position when it is displaced from it. This restoring force is proportional to the displacement, resulting in a periodic motion around the equilibrium point.

## 3. What are some examples of harmonic oscillators?

Some examples of harmonic oscillators include a simple pendulum, a mass-spring system, and a vibrating guitar string. These systems all have a restoring force that follows a sine or cosine function, resulting in simple harmonic motion.

## 4. What is the equation for a harmonic oscillator?

The equation for a harmonic oscillator is given by F = -kx, where F is the restoring force, k is the spring constant, and x is the displacement from the equilibrium position. This equation is also known as Hooke's law.

## 5. How is a harmonic oscillator different from a non-harmonic oscillator?

A harmonic oscillator follows a sinusoidal pattern of motion, while a non-harmonic oscillator does not. Non-harmonic oscillators have restoring forces that do not follow a simple mathematical function, resulting in more complex motion patterns.

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