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

 

 

 

 

You can download the App BioProfe READER to practice this theory with self-corrected exercises.