Understanding Vibrations and Harmonic Motion in Physics

Vibration: Periodic Motion

Periodic motion occurs when the magnitude that characterizes it repeats at regular intervals of time. Examples include the Moon orbiting the Earth and a piston in an internal combustion engine. In periodic motion, the period is defined as the time that passes until the motion repeats.

Oscillatory Movements

An oscillatory movement is a motion in which the path is covered in two directions. An example is a pendulum. Many oscillatory movements in nature eventually stop due to friction. These oscillations are called damped oscillations, in contrast to those that do not involve friction, which are called free oscillations.

Dynamics of Simple Harmonic Motion

Work Done by a Constant Force

The work done by a constant force is the product of the force acting on a body and the displacement that this force causes (measured in joules).

Theorem of Kinetic Energy, Work, and EC

Kinetic energy is possessed by a body by virtue of its motion. The work done by a force equals the change in kinetic energy experienced by a body, whether the force is constant or variable.

Conservative Forces

Conservative forces are those whose work between two points is independent of the path taken. The work of a conservative force along any closed path is zero. Weight, the force of gravity, elastic force, and electric force are conservative forces.

Nonconservative Forces

Nonconservative forces are those whose work done between two points depends on the path taken. If we calculate the work of these forces along a closed path, it will be different from zero, and the value depends on the path taken. Examples include frictional force and magnetic force.

Theorem of Work and Potential Energy

When all forces acting on a body are conservative, we can define a function that depends on the body's position. This function is called potential energy. The work of the conservative force between two points is equal to the negative of the variation of the potential energy.

Harmonic Motion

Vibration is a characteristic quantity that can be represented with sinusoidal and cosinusoidal functions. The simplest form is simple harmonic motion.

Simple Harmonic Motion

Suppose a particle is in uniform circular motion and projects its successive positions along the vertical axis "y". As the pulse is constant, "a" is proportional and opposite to the elongation. This property is the kinematic definition of the motion.