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# Period of a loaded Cantilever (D, DCP, CE)

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Introduction

Period of a Loaded Cantilever

Design

Aim: To investigate the relationship between the mass loaded on a cantilever and the period of oscillation of a loaded cantilever

Variables:

Independent variable: Mass loaded on a cantilever

Dependent variable: Period of oscillation of the cantilever

Control variables:

 Amplitude Maximum displacement of the end of the cantileverCan be kept constant by measuring the amplitude of each trial Length of the cantilever Can be kept constant by measuring the length of the cantilever or using the same model through the experiment Air resistance Different width of cantilever may have different air resistance. Kept constant by using a cantilever with the same cross-sectional area or simply use the same cantilever throughout the experiment. Carry out the experiment at room air density. Stiffness of the cantilever Kept constant by using the same cantilever of the same material throughout the experiment

Apparatus:

 1 2 Meter sticks One Meter stick as a cantilever and the other to measuring the amplitude of oscillations 2 Masses Masses to be loaded on the cantilever as the independent variable in this experiment 3 Stopwatch To measure the time needed for 10 number of oscillation with different mass loaded on the cantilever 4 Tapes To stable the masses on the meter stick so that the masses will not fall during the oscillation 5 Scissor To cut the tapes

Method

1. Set up apparatus as shown in the graph.

Middle

2.54

2.81

2.72

2.67

0.1

150.0

3.01

3.13

3.06

3.12

3.16

3.10

0.08

200.0

3.41

3.57

3.55

3.83

3.66

3.60

0.2

250.0

4.25

4.22

4.12

4.18

4.25

4.20

0.07

Mean:

0.2

The uncertainty of the measurement is taken to half of the smallest division of the measuring instrument. For example, the uncertainty is 0.05g for an electronic balance, 0.005 s for the stopwatch and 0.05cm for the meter stick.

The random uncertainty of the average time taken for 10 oscillations was found by half of the range of the repeats. Eg. Random uncertainty at of time taken at mass of 50g ± 0.05g is (2.63-1.94)/2 = 0.3 (taken to the nearest 1 sig. fig.)

Data Process

In this experiment, it is aimed to investigate the relationship between period and the mass loaded on a cantilever. Period is time taken for one oscillation. However, in this experiment, the time is taken to 10 oscillations, therefore, I have to divided the time taken by 10. The absolute uncertainty of the time taken by the stopwatch is still ± 0.

Conclusion

Oscillation

It was also difficult for our eyes to determine accurately the ending point of a period while the meter stick was oscillating at relatively small amplitude. To improve, the amplitude of the oscillation can be increased so that the amplitude can be measured more accurately.

Amplitude

There were random uncertainties involved in measuring the maximum amplitude of the oscillation with a meter stick. Before the oscillation, the end of the meter stick is pulled downwards with various displacements by the different weights/masses due to gravity. When oscillating, the upward and downward displacements may not be proportional, which means that meter stick is not at simple harmonic motion. The amplitude (maximum displacement) is difficult to be kept constant. For improvement, we can calculate the average amplitude by measuring the starting and ending amplitude. The amplitude should be kept constant throughout the experiment.

Bibliography

Natural Frequency and Resonance. (n.d.). Home | College of Engineering and Computer Science. Retrieved January 17, 2012, from http://www.cs.wright.edu/~jslater/SDTCOutreachWebsite/nat_frequency.htm

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