1. Principles of Dynamics
A mechanical vibration is the motion of a particle or a body which oscillates about a position of equilibrium.
The analysis of vibrations has become increasingly important in recent years owing to the current trend toward higher-speed machines and lighter structures
A mechanical vibration generally results when a system is displaced from a position of stable equilibrium. The system tends to return to this position under the action of restoring forces (either elastic forces, as in the case of a mass attached to a spring, or gravitational forces, as in the case of a pendulum).
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2. The time interval required for the system to complete a full cycle of motion is called the period of the vibration.
The number of cycles per unit time defines the frequency, and the maximum displacement of the system from its position of equilibrium is called the amplitude of the vibration.
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3. When the motion is maintained by the restoring forces only,
the vibration is said to be a free vibration.
When a periodic force is applied to the system, the resulting motion is described as a forced vibration.
When the effects of friction can be neglected, the vibrations are said to be undamped. However, all vibrations are actually damped to some degree. If a free vibration is only slightly damped, its amplitude slowly decreases until, after a certain time, the motion comes to a stop.
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4. FREE VIBRATIONS OF PARTICLES. SIMPLE HARMONIC MOTION
Consider a body of mass m attached to a spring of constant k Since at the present time we are concerned only with the
motion of its mass center, we will refer to this body as a particle.
When the particle is in static equilibrium, the forces acting on it are its weight W and the force T exerted by the spring, of magnitude
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15. Determine the amplitude of the displacement and natural frequency for
Example:
Determine the amplitude of the displacement and natural frequency for
the simple harmonic motion system
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16. the simple harmonic motion system
Example:
Determine the natural frequency in (rpm) and the amplitude of velocity for
the simple harmonic motion
system
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