forced harmonic motion

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Classification Of VibrationUndamped VS Damped


-A linear spring is a type of mechanical link thatis generally assumed to have negligible mass and damping.

Mass or Inertia Elements- The mass of inertia element is assumed to be a rigid body. It can gain or lose kinetic energy whenever the velocity of the body changes.


Damping ElementsThe mechanism which the vibrational energy is gradually converted into heat or sound known as damping.

The Tacoma Narrows bridge collapsed due to wind induced vibration on November 7th, 1940. Resonance is a process in which an object's, in this case a bridge's, natural vibrating frequency is amplified by an identical frequency.

Resonanceis a phenomenon that occurs when a given system is driven by another vibrating system or external force tooscillatewith greateramplitudeat a specific preferentialfrequency.

In this case the identical frequency was caused by strong wind gusts blowing across the bridge, creating regions of high and low pressure above and below the bridge (Bernouli's principle).

As the wind's intensity increased, the bridge rolled in a corkscrewing motion faster and faster until it was ripped apart.


In forced vibration there is an external force acts on the system. This external force which acts on the system executes the vibration of the system.

Examples of forced vibrations are air compressors, I.C. engines, turbines,machine tools etc,.

The external force may be harmonic and periodic, non-harmonic and periodic or non periodic. In this report , only external harmonic forces acting on the system are considered.

Forced Harmonic Motion Modelling-Used for analysis of forced vibrations system through a spring-mass system as amodelof a real engineering system.-Is a simple method that involves replacing the distributed mass or inertia of the system by a finite number of masses or rigid bodies.

Modelling spring mass system :The masses are assumed to be connected by massless elastic and damping members. Linear (or angular) coordinates are used to describe the motion of the masses(or rigid bodies).Such models are coordinates necessary to describe the motion of the lumped masses used in the model , the higher the accuracy of the resulting analysis.

External Forcingmodels the behavior of a system which has a time varying force acting on it. An example might be an offshore structure subjected to wave loading.Base Excitationmodels the behavior of a vibration isolation system. The base of the spring is given a prescribed motion, causing the mass to vibrate. This system can be used to model a vehicle suspension system, or the earthquake response of a structure.Rotor Excitationmodels the effect of a rotating machine mounted on a flexible floor. The crank with small mass rotates at constant angular velocity, causing the massmto vibrate.

Equation of Motion for External Forcing

Newtons law of motion gives:

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