RECENT ASSIGNMENT

Aim
The aim of the experiment is to determine the vibration characteristics of a steel beam, suspended on resilient springs. The experiment is concerned with the estimation of the generalised mass, damping coefficient, critical damping, and stiffness of the system.
2. Experimental Setup
The equipment to be used to carry out this experiment is shown in the diagram below.

3. Experimental Procedure
Measure: the response of the system in terms of period. Take measurements for the setup without additional mass and then add 1 kg at a time. Repeat measurements for each case. Assume SMALL damping.
Calculate: generalised mass, and stiffness of the system from the experimental result
1. Report Data Table
?m t f_n ?_n 1/(?_n^2 )
kg s Hz Rad/s
0 0.079 12.658 79.533 0.00015
1 0.088 11.363 71.395 0.00019
2 0.089 11.235 70.592 0.00020
3 0.097 10.309 64.773 0.00023
4 0.101 9.901 62.209 0.00025
5 0.105 9.523 59.834 0.00027
4 0.098 10.204 64.113 0.00024
3 0.099 10.101 63.466 0.00024
2 0.088 11.363 71.395 0.00019
1 0.086 11.627 73.054 0.00018
0 0.083 12.048 75.398 0.00017
Note to the tutor !!! the values in red are the actual measured values. From those I calculated fn, wn, and 1/wn square myself. I need to find m and K from the graph as shown below. Also, need to plot a new graph. The graph shown here is only demonstration how to get k and m!
I need a new graph and value of k and M.
2. Graphical representation of results
?_n=v(k/((m+?m))) Rearranging (m+?m)=k(1/(?_n^2 ))
Have to find m and k from (m+?m) vs (1/(?_n^2 )) graph
INSERT YOUR OWN GRAPH HERE
(m+?m)

?m=5
?m=4
?m=3
?m=2
?m=1
?m=0 (1/(?_n^2 ))
m
3. Report calculations
7. Report discussion
Discuss the results