The paper “ Oscillatory Behaviors of Dynamic Systems” is an engrossing version of the lab reports on engineering and construction. Oscillatory behaviors of dynamic systems encompass a lot. It is important to note that bodies that have elasticity and mass are having the capability of vibrating. With mechanical vibration in this case, therefore, bodies, pulley, for instance, are treated like ones that are elastic instead of rigid. The second aspect to note is that bodies have mass as well. The mass they possess, pulley, by virtue of their velocity, can have kinetic energy.
As this is one aspect to be noted, the analysis of a single degree of freedom system for free vibrations becomes another aspect. This is why it is advisable that before the analysis of the system is done, simplification of the system by modeling should be done. (Ryder and Bennett, 23) also advises that when handling a pulley system having one degree of freedom a lumped mass is easier to deal with as compared to distributed mass. This is because the determination of the dynamic behavior of a lumped mass by one independent principal coordinate is easier than the former.
With all these aspects, this project will critically analyze, through elements of mechanical vibration, a single degree of freedom pulley for free vibrations as shown in the diagram below. Mechanical ExpressionsThe mechanical expression of this project is going to be analyzed based on the figure below. Before embarking on practical calculations that entail the aspect of Pulley system having one degree of freedom, the definition of terms that will be commonly referred to is important. To begin with, (Ryder and Bennett, 23) defines the degree of freedom of a pulley as the number of independent coordinates that the pulleyPreambleThe figure above consists of a pulley that has been assembled to pull a load.
The spring labeled K is used to impose the motion that is going to pull the load M2. Another point is that as per the figure above, K represents stiffness which also represents a flexible connection to the pulling force. Then there is the damping coefficient at M2 represents drag between the mass pulled and the shaft walls. Definition of terms related to the figure aboveNatural frequencyWithin the context of a pulley system above, this project will need to recognize the fact that there is only one degree of freedom since the movement of the mass is dependent on the motion of the mass.
The second aspect is the natural frequency, according to Beards (207), the natural frequency is the point when the system above can be able to execute free vibration which is not damped. Natural frequency is the point at which the pulley is able to vibrate naturally once it is set to move. Static Equilibrium PositionThe project will set up the figure above in such a manner that the Static Equilibrium Position (SEP) will mean that there is no motion of the mass (M2) or external agent holding the spring.
Therefore at the SEP spring, K, as represented above, will be deflected since it will have to support at least 50% of the mass (M2)
Beards, C.F., Engineering Vibration Analysis with Application to Control Systems, Arnold, 034063183X (1999). Print
Ryder, G.H, and Bennett, M.D. Mechanics of Machines, 2, Industrial Press, Inc., 083113030X. (2000). Print