Introducción a las vibraciones mecánicas – ED del movimiento armónico simple

Introduction to Mechanical Vibrations

Overview of Mechanical Vibrations

• A mechanical vibration is defined as the movement of a particle or body oscillating around an equilibrium position, such as an unbalanced motor or a bridge affected by strong winds.

• Most vibrations in machines and structures are undesirable due to increased stress and energy losses, potentially causing irreversible damage.

Types of Vibrations

• Vibrations occur when a system deviates from a stable equilibrium position; they can be classified into free vibrations (maintained by restoring forces) and forced vibrations (resulting from periodic external forces).

• When friction effects can be ignored, the vibrations are termed undamped. The discussion will cover these three types in future videos.

Simple Harmonic Motion

Understanding Simple Harmonic Motion

• The focus shifts to simple harmonic motion, considering a mass attached to a spring with constant k . Initially, the spring is at equilibrium without any mass.

• When a test mass is added, it deforms the spring by a static displacement referred to as delta .

Forces Acting on the Mass

• At static equilibrium, the weight ( W ) of the mass equals the force exerted by the spring ( F = k cdot delta ).

• If the particle moves away from its equilibrium position by distance x_n , it generates oscillation characterized by amplitude x_m .

Analyzing Oscillatory Motion

Force Analysis in Oscillation

• Considering forces acting on the particle at position P , where total force equals weight minus spring force plus displacement.

• This leads to an equation derived from Newton's second law: sum of forces equals mass times acceleration.

Deriving Key Equations

• The resulting equation reflects that acceleration is proportional to displacement but in opposite direction—this defines simple harmonic motion.

• The established relationship indicates that for simple harmonic motion, acceleration relates directly back to displacement through Hooke's Law.

Conclusion on Simple Harmonic Motion Characteristics

Summary of Findings