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# Public Formula Library

### HARMONIC OSCILLATOR

Just for viewing purposes. You can store and calculate this formula only inside the application.

### Formula name

HARMONIC OSCILLATOR

### Description

simple harmonic oscillator

### Syntax

/*

t: time at which the displacement, velocity and acceleration are computed

A: amplitude

w_0: angular frequency of the oscillator

Φ: Phase, determines starting point /conditions at time t=0 */

/*displacement at time t */

x_t = A*COS(w_0*t + Φ)

/* velocity at time t */

v_t = -A*w_0*SIN(w_0*t-Φ)

/*acceleration at time t */

...

t: time at which the displacement, velocity and acceleration are computed

A: amplitude

w_0: angular frequency of the oscillator

Φ: Phase, determines starting point /conditions at time t=0 */

/*displacement at time t */

x_t = A*COS(w_0*t + Φ)

/* velocity at time t */

v_t = -A*w_0*SIN(w_0*t-Φ)

/*acceleration at time t */

...

### Notes

A harmonic oscillator is a system in which the restoring force is direct proportional to the displacement, such as a mass attached to a spring.

### Category / Subcategory

Physics / Kinematics

### Creator

pbrodmann@brodmann.biz

### Account

Free

### Tags

oscillator velocity and acceleration

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