## Anharmonic oscillator

When the restoring force is not proportional to the displacement from equilibrium position, the system is said to be an anharmonic oscillator. As a result, anharmonic oscillator motion is not solely sinusoidal, and therefore cannot be adequately captured by a simple linear differential equation.

## Examples of anharmonic oscillator

The examples of anharmonic oscillators is given below :

- An anharmonic oscillator with a cubic potential
- An anharmonic oscillator with a quartic potential:

### An anharmonic oscillator with a cubic potential:

This can be modeled by a potential energy function that show diversion from a quadratic potential, such as

V(x) = 1/2 kx^{2} + λx^{3},

where

- λ=constant that determines the strength of the cubic term.

The nonlinearity of the cubic term made the oscillator motion anharmonic, with a frequency that changes with the changing amplitude of the oscillation.

### An anharmonic oscillator with a quartic potential:

This can be modeled by a potential energy function that diverges from a quadratic potential, such as

V(x) = 1/2 kx^{2} + αx^{4},

Where

- α=constant that determines the strength of the quartic term.

The oscillator’s motion is anharmonic due to nonlinearity of the cubic term, with a frequency that depends on the oscillation’s amplitude

## Characteristics Of Anharmonic Oscillator

The characteristics of an harmonic oscillator is given below:

- Nonlinear restoring force:
- Non-sinusoidal motion:
- Non-constant frequency
- Multi-frequency motion:
- Energy dissipation:

### Nonlinear restoring force:

A nonlinear restoring force is one that is not directly proportional to the displacement from the equilibrium position of an anharmonic oscillator.

### Non-sinusoidal motion:

Motion of an anharmonic oscillator is not fully sinusoidal, hence it cannot be modelled by a simple

- sine or
- cosine function.

### Non-constant frequency:

The frequency of anharmonic oscillator’s frequency is changing and dependent on the system’s beginning

- Circumstances
- and amplitude.

### Multi-frequency motion:

An anharmonic oscillator can display multi-frequency motion, which means it can oscillate at several frequencies at once.

### Energy dissipation:

An anharmonic oscillator may experience energy dissipation, which is the gradual loss of the system’s energy to outside influences. This may result in damping or decay when the oscillations’ amplitude gradually decreases.