undamped free vibration
OBJECTIVE
To determine the natural frequency for an undamped spring mass system.
INTRODUCTION
Vibration is the periodic motion of a body or system of connected bodies displaced from a position of equilibrium. It is a mechanical phenomenon whereby oscillations occur about an equilibrium point. The oscillations may be periodic or random. Free vibration occurs when a mechanical system is set off with an initial input and then allowed to vibrate freely. If there is no external force applied on the system, the system will experience free vibration. Motion of the system will be established by an initial disturbance. Furthermore, if there is no resistance or damping in the system, the oscillatory motion will continue forever with constant amplitude. Such a system is termed undamped. In this experiment the natural frequency for an undamped spring mass system is to be determine by using a mass-spring-damper.
THEORY
Newton’s 2nd law
…………………….………. ( Equation 1 )
Hence, ………………….……... ( Equation 2 )
Rearrange Equation 2
.………..………………... ( Equation 3 ) where natural frequency of the system, …..…….………..........……... ( Equation 4 )
APPARATUS
Displacement measuring transducer and displacement measuring plate, spring, weights, loading rod.
PROCEDURE
Determine the stiffness of the spring The length of the unloaded spring was measured. A weight was inserted unto the loading rod (with plate), then the loading rod was anchored to the spring. The extension of the loaded spring was noted. Steps 2 to 3 were repeated with four other different loading conditions.
Determine the natural frequency of the spring-mass system A weight was inserted unto the loading rod (with plate), then the loading rod was anchored to the spring. The displacement transducer was arranged in such a manner that the probe is at right angle to the plate on the loading rod. The ‘quickDAQ’ was run on the PC then the ‘Sample Rate per Channel’ was set
To determine the natural frequency for an undamped spring mass system.
INTRODUCTION
Vibration is the periodic motion of a body or system of connected bodies displaced from a position of equilibrium. It is a mechanical phenomenon whereby oscillations occur about an equilibrium point. The oscillations may be periodic or random. Free vibration occurs when a mechanical system is set off with an initial input and then allowed to vibrate freely. If there is no external force applied on the system, the system will experience free vibration. Motion of the system will be established by an initial disturbance. Furthermore, if there is no resistance or damping in the system, the oscillatory motion will continue forever with constant amplitude. Such a system is termed undamped. In this experiment the natural frequency for an undamped spring mass system is to be determine by using a mass-spring-damper.
THEORY
Newton’s 2nd law
…………………….………. ( Equation 1 )
Hence, ………………….……... ( Equation 2 )
Rearrange Equation 2
.………..………………... ( Equation 3 ) where natural frequency of the system, …..…….………..........……... ( Equation 4 )
APPARATUS
Displacement measuring transducer and displacement measuring plate, spring, weights, loading rod.
PROCEDURE
Determine the stiffness of the spring The length of the unloaded spring was measured. A weight was inserted unto the loading rod (with plate), then the loading rod was anchored to the spring. The extension of the loaded spring was noted. Steps 2 to 3 were repeated with four other different loading conditions.
Determine the natural frequency of the spring-mass system A weight was inserted unto the loading rod (with plate), then the loading rod was anchored to the spring. The displacement transducer was arranged in such a manner that the probe is at right angle to the plate on the loading rod. The ‘quickDAQ’ was run on the PC then the ‘Sample Rate per Channel’ was set