## Oscillations theory

# Oscillations

Oscillations are the repetitive variation, disturbance or fluctuation over the time measure about a central value or system. A particle oscillates periodically when it moves relative to its equilibrium position.

Simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement.

It can serve as a mathematical model of a variety of motions, such as the oscillation of a spring. In addition, other phenomena can be approximated by simple harmonic motion, including the motion of a simple pendulum as well as molecular vibration. There are several key concepts in the study of harmonic motion:

- –
__Amplitude__(A): maximum elongation which a stroke has. - –
__Period__(T): time that a complete swing is done. - –
__Frequency__(f): Number of oscillations per unit time.

The driving force acting on a particle of mass m so that it oscillates with simple harmonic motion, must be proportional to the displacement x and opposite to it.

**FORMULA SUMMARY:**

Mobile position that it describes

Mobile velocity which is subjected to a harmonic force

Mobile accelerating mobile subjected to a harmonic force

Force that has to act on a particle so that it oscillates with simple harmonic motion

Harmonic motion of translation

Harmonic motion of rotation

Period of simple pendulum (L = pendulum length)

Period of physic pendulum (d = distance between the center of gravity and the point of suspension)

Reduced length of a physical pendulum

**ENERGY OF SIMPLE HARMONIC MOTION**

The forces involved are central and conservative; therefore, the mechanical Energy is constant

Potencial Energy

Kinetic Energy

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