# Simple Harmonic Motion Julie Jones

September 9, 2016

Lab Partner: John Jackson Lab TA: Robert Schmitz

Introduction:

When a mass is hung from a spring Hooke’s Law tells us it will stretch by an amount inversely proportional to the spring constant, k, which is a characteristic of the spring. Furthermore, if pulled down and released, the mass (m) will oscillate at angular frequency ω2 = k/m. In this lab we hung masses from a spring to first determine the spring constant, then allowed the masses to oscillate so we could compare our measured and theoretical angular frequencies.

Results

The measured value of our spring constant was 145 ± 1.85 N/m. The uncertainty in our result was due to measurement uncertainty; the meter stick was marked in millimeters, which limited our accuracy to ±1 mm.

The 0.8 kg mass had an expected angular velocity of 13.5 ± 0.2 rad/s and our measured value was 13.6 ± 0.3 rad/s. The 1.3 kg mass had an expected angular velocity of 10.6 ± 0.1 rad/s and our measured value was 10.7 ± 0.2 rad/s. The 1.7 kg mass had an expected angular velocity of 9.2 ± 0.1 rad/s and our measured value was 9.3 ± 0.2 rad/s. In all cases the expected and measured values agreed within the uncertainties.

All three masses oscillated at frequencies slightly higher than the calculated values. This may be an indication that the spring is not completely ideal. However the differences between the measured and calculated frequencies are very small compared to the values themselves therefore if the spring is not ideal the deviation is minimal.

Conclusion

The spring followed Hooke’s Law closely and when we used our calculated spring constant to predict oscillation angular frequencies we found they agreed within uncertainties to the measured frequencies. We concluded the spring used in this lab is very close to ideal.

This is an example lab report (describing a nonexistent lab), designed to illustrate the format and length of a typical lab report. Use both this report and the guideline on Blackboard to improve the quality of your own reports. The first page is the actual report. The last two pages are the data that was collected (and graded) during the lab itself.

Mass Displacement Force Spring Constant

m (kg) x (m) % Uncertainty1 F = mg (N) k = F/x (N/m) Uncertainty2

(N/m) 0.800 0.055 1.820 7.84 143 2.59 0.800 0.054 1.850 7.84 145 2.69 0.800 0.054 1.850 7.84 145 2.69 1.300 0.089 1.120 12.74 143 1.61 1.300 0.090 1.110 12.74 142 1.57 1.300 0.088 1.140 12.74 145 1.65 1.700 0.115 0.870 16.66 145 1.26 1.700 0.112 0.893 16.66 149 1.33 1.700 0.114 0.877 16.66 146 1.28

Average 145 1.85 Std. Dev. 2.00

1) Uncertainty in measurement of the displacement (m): 0.001 2) % Uncertainty * Calculated Value / 100 Calculated Value of Spring Constant (N/m): 145 +/- 1.85