CC-logbook Lab 6.docx

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PHYSICS LOGBOOK TEMPLATE G Experiment logbook . Include your work from this week’s lab here. You will use this logbook later in the semester when you write your lab report. Lab Date: 11 / 5 /2023 Team : GROUP 9, Jack obrien, Max Meggitt Tutor: Tim

Checkpoint 1: Logbook 1.1 Measure the diameter of the wire in several places and calculate the linear density μ and its uncertainty. Your diameter measurements should not vary by more than ±0.01 mm. Measurement Length Measured mm Uncertainty 1 0.79 ±0.01 mm 2 0.81 ±0.01 mm 3 0.82 ±0.01 mm 4 0.87 ±0.01 mm 5 0.83 ±0.01 mm Average 0.824 ±0.01 mm u = 0.004159479 Logbook 1.2 Using Equation 4 (found in the Appendix) calculate the expected (theoretical) fundamental frequency f1, corresponding to three values of tension, say 10 N, 30N and 90 N. Check with a tutor that your linear density calculation is correct before plotting your graph. f10 = 24.51605214 f30 = 42.46304791 f90 = 73.54815642

Logbook 1.3 Plot your predicted results of f versus T in Excel. Do this first on a linear scale and then use ‘Format axis’ to select ‘Logarithmic axis’ on both axes. Set minimum values to 10 on both axes, and add minor gridlines and axis labels. Add a power-law trendline and confirm that the slope of the line is 0.50. Logbook 1.4 Use your graph of theoretical resonant frequency against tension to predict the expected values of resonant frequency for FIVE tensions, increasing from 3 to 7 masses.

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Checkpoint 2: Logbook 2.1 Experimentally determine the fundamental frequency for the FIVE tensions you predicted values for in Log-book 1.4. Leave the input voltage at 1.0 V pp . The location of the resonance requires careful (slow!) adjust-ment of the frequency about the predicted values. This was done Logbook 2.2 Make a logarithmic plot (as you did in Logbook 1.3) of your measurements and predictions of resonant frequency against tension. Use a different colour to distinguish your measurements from the predictions. Draw a line of best fit through the experimental points. Estimate the slope and its uncertainty using the LIN-ESTfunction(you will need to take the log of your data before using LINEST).

Compare the two lines. Comment on how well the simple theoretical model in Equation(4) describes the actual behaviour of the vibrating wire. Are there any systematic differences between theoretical and experimental values? Both lines have a similar gradient ~0.5, and follow the simple theoretical model in equation 4. It demonstrates that as the tension of the wire is increased the vibrating wire’s frequency increases. The only difference between the two is that the recorded values are slightly less than the theoretical values. It should be noted that the linear equation used to predict frequency is an over simplified equation and doesn't take into account background noise, heat and rust on the wire.

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Checkpoint 3: Logbook 3.1 Keeping the tension and length of the wire constant (use between 3 and 7 weights), excite the fundamental and higher modes of vibration. Measure the frequency corresponding to each mode number. To detect the higher modes you will need to increase the input signal to the maximum. Measure the odd harmonics out to the 13th harmonic (or beyond if you have time), leaving the magnet and detector fixed at the midpoint. they were measured Logbook 3.2 Plot a graph of measured frequency as a function of mode number n along with a plot of: f ∝ n. Using Equation (4) from Appendix I, graph a theoretical prediction of f as a function of n.

Logbook 3.3 Equation (5) in Appendix I is equivalent to Equation(4), but takes into account the bending of a stiff wire for different modes of oscillation. By programming Equation (5) into Excel calculate this non-linear model prediction of harmonic frequency. Logbook 3.4 Are your results more consistent with those predicted from Equation (4) or Equation (5)? Is there any evidence that Equation (4) does not predict all of your results? Discuss. Equation 4 showed similar results but as the nodes increased, the inaccuracy also increased. Equation 5 proved to be more accurate to the experimental results. E.g., the experimental result for node 11 was 731Hz; equation 4 produced a result of 704.1, and equation 5 produced a result of 734, which is off by a difference of 4, not 26.9. Thus, we can more accurately derive our results when taking into account more variables such as the thickness and stiffness of the wire.

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