b_simple pendulum2 rev.pdf

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CURTIN UNIVERSITY OF TECHNOLOGY

Faculty of Science and Engineering

DEPARTMENT OF IMAGING AND APPLIED PHYSICS

AN INVESTIGATION OF THE SIMPLE PENDULUM

SCIENTIFIC AIMS

To measure the period of a simple pendulum to the greatest possible precision and hence to

determine a value for g, the acceleration due to gravity.

To investigate how the period of the simple pendulum varies with mass of the pendulum bob

and the amplitude of the swing.

LEARNING OUTCOMES

Plotting data with uncertainties and drawing a line of best fit*

Determine the value of g from the slope of the line of best fit and the associated uncertainty in g

Compare the measured value with the accepted value of g

*See The Use of Graphs in this Lab Manual for graphing

APPARATUS

Pendulum, string, clamp, metre rule, stop watch, balance

THEORYA Simple Pendulum is an ideal pendulum consisting of a point mass m, (the bob), suspended

from a light (weightless) string, length . The period is the time taken for the pendulum to

complete one complete oscillation, i.e. in the diagram below for the pendulum to go from A to B to

C to B and back to A. Alternatively the pendulum could go from B to C to B to A and back to B

again.

bob

A

B

C

D


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The amplitude is the maximum angular displacement from equilibrium. Due to energy losses

the amplitude decreases with time.

For small amplitudes (how small is small?), the period of the simple pendulum can be shown to

be very nearly independent of the mass of the bob and the amplitude of its swing and is then given

by:

T = 2g

...................................... (1)

Where g is the acceleration due to gravity.

The aim of this experiment is to verify these aspects of the behaviour of the simple pendulum.

EXPERIMENTAL PROCEDURE

1. Suspend a pendulum using the clamp provided and measure its period. Discuss in your group

how you can maximise the accuracy of your measurement. For instance consider the number

of oscillations timed, the position where timing should begin, etc.Make a few preliminary measurements of the period.

2. Estimate the uncertainty in your measurement of the period.

3. The period could depend on several factors, e.g. the amplitude of the swing and the mass of

the pendulum bob. Discuss these and any other factors that could affect the period. Make

some notes.

4. PART 1. Investigate how the period of the simple pendulum T varies with the length l of the

pendulum keeping all the other variables constant. (Other variables are mass of the

pendulum bob m and the amplitude of swing, ) Make angle of the swing small (about 10

to 15)

5. Under the heading DATA construct a table for your results similar to that shown below and

enter your measurements. As part of the data collection process ensure that you have

measured the periods for at least five different lengths.

Mass of the pendulum bob =

Amplitude of oscillations =

length, (m)

Time for Noscillations

(s)

Number ofcomplete

oscillations

Period, T(s)

T

(s2)


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6. PART 2. Investigate how the period of the simple pendulum T varies with the mass of the

pendulum bob m keeping all the other variables constant.

Length of the pendulum =

Amplitude of swing =

Mass of pendulumbob

(kg)


(s)

Number ofcomplete

oscillations

Period, T(s)

T

(s2)

7. PART 3. Investigate how the period of the simple pendulum T varies with the amplitude of

the pendulum keeping all the other variables constant.

Length of the pendulum =

Mass of the pendulum bob =

Amplitude ofswing,

(deg)


(s)

Number ofcomplete

oscillations

Period, T(s)

T

(s2)

For Part I, plot a straight-line graph to show that T (the period) and (length of pendulum)are related as described by eqn (1). Does your line of best fit pass through the origin (T = 0;

= 0)? If not, what could be a possible explanation? If not, would that affect the results of

your analysis in 8(a) below?

Similarly plot graphs for Part II and III and comment how the value of g would be affected bychanging the mass of the pendulum bob and the large amplitude of swing.


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NOTE

1. You should never force your line of best fit to go through the origin.

2. It is normal practice to plot the uncertainties on the data points. Can you do so in this

experiment?

8 (a) Under the heading CALCULATIONS use the gradient of your graph to determine the

acceleration due to gravity, g and its uncertainty.

From Eqn (1)

T2 = 42 / g

So if m is the gradient of the graph of T2 versus , then m = 42/ g and hence

g = 42/ m

8(b) Present your results and their uncertainties for the measurements in Tables as shown in

sections 5, 6 and 7.

9. Under the heading DISCUSSION compare your result for g to the accepted value (you must

quote a reference for the accepted value of g). Comment on the significant errors and how

they might be reduced. Discuss your findings with regard to the dependence of the period T

on the mass of the bob and the amplitude of its swing.

10. Provide a CONCLUSION.

===================================================================

TIME FORREFLECTION

The purpose of this experiment was to:

A. Introduce you to the following concepts

1.A record of observations

2.The structure of a laboratory report

3.Experimental uncertainty

B. Further investigate measurement uncertainty, for instance by

1. Assigning an uncertainty to an observation.

2. Propagating uncertainty through a calculation

C. Introduce the graphical presentation of experimental data and deductions that can be made

from it. e.g. for the determination of g, the acceleration due to gravity from the gradient of a

line

b_simple pendulum2 rev.pdf

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