Free The Apparatus Set-Up Looks Like The Following: Report Sample

The aim of this experiment is to be able to measure experimentally the natural frequency and the damping of an object, in this case a beam. The beam is subjected to bending and releasing, in which way the beam would oscillate. The movement of the beam is recorded using a pen connected to the free end of the beam, and the pen in contact with a chart recorder. The natural frequency is estimated by measuring the time interval between two successive peaks of the oscillations, then getting the reciprocal of this value. The damping is estimated by getting the ratio of the first and second peaks, then getting the natural logarithm of this ratio.

Figure 1. Experimental Setup

The measured velocity is:

v=lengthmtimes=62.56 mm3.32 s=18.84 mm/s
The period T is measured by measuring the distance between two successive peaks, and then dividing the value by the speed of paper:
T=distancev=

Thus, the natural frequency is derived by getting the reciprocal of the period:

f=1T=

For the setup with the damping dashpot, the table of results is shown in the following:

Without the dashpot, the measured peaks are:
Thus, the damping of the beam is:
The measured frequency for the system with dashpot shows desirable precision among the measurements. The values are within small margins of each other, which show why the calculated damping average is accurate, and all the frequency estimates are the same. The damping changed when the dashpot was added. Moreover, changing the setup from “holes open fully” to “holes open partially” has almost doubled the damping value.
This experiment can be further improved by minimizing human intervention with the apparatus. The bending and releasing of the beam using hands can be replaced by a robotic arm that could apply a more accurate amount of bending distance. Also, the distance measurements can be measured by more accurate means of measurement, other than a ruler.
It was observed that the natural frequency of the beam is the same with or without the dashpot.