Experiment 21

Experiment 21 - f o f m Err 1.22 Hz 1.28Hz 4.69...

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Experiment 21: Forced Oscillations and Resonance in a Simple Harmonic Motion System (i) 2πf o = (k/M) 1/2 T = 2π√(M/k), 1/f o = T 1/f o = 2π√(M/k) f o = (1/2π) √(k/M) 2πf o = (k/M) 1/2 (ii) Dr. Placek told us not to worry about answering this question. (iii) Both are a result of excitation of the resonant frequency of the object. In the case of the Tacoma Narrows Bridge, the wind caused vibrations at resonant frequency. Because of insufficient damping, the amplitude of those vibrations got very large and in turn caused the bridge to collapse. As for the glass, the resonance may not be as strong but if excited by external pressures at that frequency (the sound wave of the soprano’s voice), it can result in a greatly magnified amplitude of vibrations which can then in turn break the glass. Table I shows the natural frequency (f o) , frequency at maximum amplitude (f m) , and percent error (% Err). Table I Frequency (Hz) Data
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Unformatted text preview: f o f m % Err 1.22 Hz 1.28Hz 4.69% Calculations: (Actual – Experimental)/Actual x 100 (1.28-1.22)/1.28 x 100 = 4.69% Table II shows frequency [Freq. (Hz)] and resultant amplitude [Ampli. (m)]. Table II Amplitude Data Freq. (Hz) Ampli. (m) 1.00 Hz 0.000 m 1.10 Hz 0.001 m 1.20Hz 0.005 m 1.28 Hz 0.015 m 1.35 Hz 0.011 m 1.40 Hz 0.005 m 1.45 Hz 0.002 m 1.52 Hz 0.001 m 1.60 Hz 0.001 m 1.70 Hz 0.000 m 1.80 Hz 0.000 m Figure I is the plot of Table II’s values. Figure I Table III shows the experimental value for frequency (expt.), when the mass of the spring is neglected (m = 0g), and when the mess of the spring is not neglected (m = 10g). Table III f o (Hz) Expt. m = 0g m = 10g 1.22 Hz 1.23 Hz 0.617 Hz Calculations: 10/8.15s = 1.23 Hz 10/16.21s = 0.617 Hz Frequency vs. Amplitude-0.005 0.005 0.01 0.015 0.02 0.5 1 1.5 2 Frequency (Hz) Amplitude (m) Series1...
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Experiment 21 - f o f m Err 1.22 Hz 1.28Hz 4.69...

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