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DavidOBrien_E3 - Sheet1 Forced Harmonic Motion Sec 0106...

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Unformatted text preview: Sheet1 Forced Harmonic Motion Sec 0106 Mbar (gm) 52.2 x (mm) 36 x 0.58 k 0.22 k (N/m) 13.61 T 0 Mspring (gm) 2.1 T (sec) 0.4 0 0.17 m=Mbar+Mspring/3 (gm) 52.9 0=2/T (rad/sec) 15.71 mw (gm) 50 Table 2 Amplitude and phase shift vs. frequency A0 (mm) 2 X0 (mm) f (Hz) 0.5 5 0.7 5 0.9 6 1.1 6 1.3 7 1.5 8 1.7 8 1.9 11 2.1 16 2.3 30 2.5 33 2.7 27 2.9 14 3.1 9 3.3 6 =2f =2f Q=X/A Q 12.73 6.37 =2f (Hz) 0 0 5 5 5 10 15 30 55 90 110 160 165 170 170 3.14 4.4 5.65 6.91 8.17 9.42 10.68 11.94 13.19 14.45 15.71 16.96 18.22 19.48 20.73 w vs. x 35 30 25 X (mm) 20 15 10 5 0 3.14 4.4 5.65 6.91 8.17 9.42 10.68 11.94 13.19 14.45 15.71 16.96 18.22 19.48 20.73 Omega (rad/sec) Page 1 10 5 0 3.14 4.4 5.65 6.91 8.17 9.42 10.68 11.94 13.19 14.45 15.71 16.96 18.22 19.48 20.73 Omega (rad/sec) Sheet1 The experiement involved measuring resonant frequency of a spring by using an oscillator to measure the phase and amplitude of the system. The natural oscillation frequency was determined and then tested using the oscillator. 2. Ran out of time because oscillator did not work. Page 2 Sheet1 m (gm) 0.02 w0 = sqrt(k/m) 0.52 0 0 X0 (theory) 2.08 2.17 2.29 3.5 2.59 Theta vs. Omega 180 160 140 Theta (Degrees) 120 100 80 60 40 20 0 3.14 4.4 5.65 6.91 8.17 9.42 10.68 11.94 13.19 14.45 15.71 16.96 18.22 19.48 20.73 16.96 18.22 19.48 20.73 Page 3 Omega (rad/sec) The 60 40 20 0 3.14 4.4 5.65 6.91 8.17 9.42 10.68 11.94 13.19 14.45 15.71 16.96 18.22 19.48 20.73 Omega (rad/sec) 16.96 18.22 19.48 20.73 Sheet1 Page 4 Sheet1 5.71 16.96 18.22 19.48 20.73 Page 5 5.71 16.96 18.22 19.48 20.73 Sheet1 Page 6 ...
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