Recent Question/Assignment
1. Aim
The aim of the experiment is to determine the natural frequencies of a beam mounted on two springs, which may be considered as a system with two degrees of freedom.
2. Experimental Setup
The equipment to be used to carry out this experiment is shown in the diagram below.
3. Experimental Procedure
For a range of frequencies (6 to 15 Hz with the step 1/2 Hz), measure using the CRO:
A1, A2, A3 and F0 - amplitudes of system response in points 1, 2, and 3, and amplitude of input force respectively;
Plot frequency response function for three points. Determine the 2 natural frequencies.
4. Report Data Table (ACTUAL DATA)
f A_1 A_2 A_3 F_o
Hz mm mm mm mm
6 0.2 0.1 0.14 constant
6.5 0.4 0.2 0.2 constant
7 0.3 0.18 0.16 constant
7.5 0.39 0.3 0.28 constant
8 0.89 0.8 0.63 constant
8.5 4.05 4 4.25 constant
9 0.75 1.05 1.495 constant
9.5 0.125 0.445 0.8 constant
10 0.027 0.425 1.2 constant
10.5 0.27 0.305 1.05 constant
11 0.52 0.285 1.2 constant
11.5 1 2.2 1.7 constant
12 2.85 1.7 3.85 constant
12.5 6.7 0.105 6.85 constant
13 2.75 0.205 2.8 constant
13.5 1.75 0.195 1.65 constant
14 1.45 0.205 1.25 constant
14.5 1.35 0.205 1.15 constant
15 1.15 0.2 0.81 constant
Example of Frequency response function for 1DoF system
Assume that you plot frequency response function as a function of ratio of natural and input frequencies. There will be a pick at instant when input frequency is equal to natural frequency of the system. This indicates a resonant frequency.
Resonance refers to the tendency of a system to oscillate with greater amplitude at some frequencies than at other frequencies. Frequencies at which the response amplitude is a relative maximum are known as resonance frequencies
5. Graphical representation of results
frequency response functions for three points shown below as follows:
Fig1: results from accelerometer A1
Fig2: results from accelerometer A2
Fig3: results from accelerometer A3
(note: I plotted the graphs from the data above and need help calculating the 2 natural frequencies and a small discussion. Thanks
CALCULATION:
Determine the 2 natural frequencies
7. Report discussion
Discuss the results:
The aim of the experiment is to determine the natural frequencies of a beam mounted on two springs, which may be considered as a system with two degrees of freedom.
2. Experimental Setup
The equipment to be used to carry out this experiment is shown in the diagram below.
3. Experimental Procedure
For a range of frequencies (6 to 15 Hz with the step 1/2 Hz), measure using the CRO:
A1, A2, A3 and F0 - amplitudes of system response in points 1, 2, and 3, and amplitude of input force respectively;
Plot frequency response function for three points. Determine the 2 natural frequencies.
4. Report Data Table (ACTUAL DATA)
f A_1 A_2 A_3 F_o
Hz mm mm mm mm
6 0.2 0.1 0.14 constant
6.5 0.4 0.2 0.2 constant
7 0.3 0.18 0.16 constant
7.5 0.39 0.3 0.28 constant
8 0.89 0.8 0.63 constant
8.5 4.05 4 4.25 constant
9 0.75 1.05 1.495 constant
9.5 0.125 0.445 0.8 constant
10 0.027 0.425 1.2 constant
10.5 0.27 0.305 1.05 constant
11 0.52 0.285 1.2 constant
11.5 1 2.2 1.7 constant
12 2.85 1.7 3.85 constant
12.5 6.7 0.105 6.85 constant
13 2.75 0.205 2.8 constant
13.5 1.75 0.195 1.65 constant
14 1.45 0.205 1.25 constant
14.5 1.35 0.205 1.15 constant
15 1.15 0.2 0.81 constant
Example of Frequency response function for 1DoF system
Assume that you plot frequency response function as a function of ratio of natural and input frequencies. There will be a pick at instant when input frequency is equal to natural frequency of the system. This indicates a resonant frequency.
Resonance refers to the tendency of a system to oscillate with greater amplitude at some frequencies than at other frequencies. Frequencies at which the response amplitude is a relative maximum are known as resonance frequencies
5. Graphical representation of results
frequency response functions for three points shown below as follows:
Fig1: results from accelerometer A1
Fig2: results from accelerometer A2
Fig3: results from accelerometer A3
(note: I plotted the graphs from the data above and need help calculating the 2 natural frequencies and a small discussion. Thanks
CALCULATION:
Determine the 2 natural frequencies
7. Report discussion
Discuss the results:
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