# An Investigation of the Simple Pendulum

An investigation of the simple pendulum

2.0 Objectives

The purpose of the experiment is to investigate the time taken on the greatest possible precision of period of simple pendulum and the value of g, acceleration due to gravity and two different periods of both big and small simple pendulum’s oscillations.

3.0 Summary of Result

The results of the experiment have proven the acceleration due to gravity and the precision of period of simple pendulum. Besides that, the length of the pendulum did influence the period and the period increased linearly with length. The results matched to within 11.00 %. Thus the experiments were all carried out successfully.

4.0 Theory

A simple pendulum consisting of a point mass m, tied to a string, length L. The period of a pendulum is also known as the time taken for the pendulum oscillates one complete cycle. To have a complete cycle, Figure 1 show the motion of pendulum when it is released. The bob will move from A to rest position to B to rest position again and lastly back to point A.

Figure 1

The starting angle, Ө is the maximum amplitude of the oscillations. The amplitude will decreases with time since the energy will losses. For small starting angle, Period of pendulum, T can be calculated by the formula below, with g as the acceleration

“T” becomes precise in the limit of zero amplitude motion and if amplitude of the motion is larger, the period T become less accurate.

5.0 Procedure

A pendulum bob was tied at the end with a string measuring 0.1m long and it is hung on a clamp stand. The pendulum was then released from the angle of 300. By using the stopwatch provided, the time taken for 10 complete oscillations was recorded. The data was then recorded in a table. Steps 1 to 4 were repeated for different lengths of string: 0.2m, 0.3m, 0.4m, 0.5m, 0.6m, 0.7m, 0.8m, 0.9m and 1.0m. (Optional Part - Angle)

A 0.4m length of string was used. The pendulum was then released from a starting angle of 300. By using the stopwatch provided, the time taken for 10 complete oscillations was recorded. The data was then recorded in a table. Step 2 to 3 was repeated for angles of 450, 600,750 and 900. (Optional Part -Mass)

The mass of 3 pendulum bob was weighed using electronic balance and recorded in a table. One of the pendulum bob was tied to the pendulum and it is then released from with a string of 0.4m length of string at a starting angle of 300. By using the stopwatch provided, the time taken for 10 complete oscillations was recorded. The data was then recorded in a table. Then the experiment was repeated by combining two pendulums bob and three pendulums with the same length of string of 0.4m and same angle of 300. 6.0 Results & Calculations

Experiment 1: Effect of Length on Time

Length(m)| Period, 10T(s)| Average Period, 10T(s)| Period, T(s)| T2(s2)| 0.1| 6.07| 6.06| 6.09| 6.07| 0.61| 0.37|

0.2| 8.03| 8.04| 8.01| 8.02| 0.80| 0.64|

0.3| 10.32| 10.31| 10.34| 10.30| 1.03| 1.06|

0.4| 12.04| 12.03| 12.06| 12.04| 1.20| 1.44|

0.5| 13.01| 13.05| 13.02| 13.02| 1.30| 1.69|

0.6| 14.36| 14.40| 14.40| 14.38| 1.44| 2.07|

0.7| 15.46| 15.49| 15.51| 15.47| 1.55| 2.40|

0.8| 16.90| 16.94| 16.89| 16.91| 1.69| 2.86|

0.9| 18.00| 18.10| 18.05| 18.05| 1.81| 3.28|

1.0| 18.75| 18.85| 18.80| 18.80| 1.88| 3.53|

∆L=0.1cm

=0.001m

ΔT=0.02s

ϴ=5°, ∆Ө=1°

T=2πlg , g=4π2/m , T2=4π2l/g

Experiment 2: Effects of mass on time

Mass(g)| Period,10T(s)| 10T(Average)| T(s)|

8.91| 15.65| 15.47| 15.47| 15.53| 1.55|

31.28| 15.28| 15.59| 15.50| 15.45| 1.55|

l=0.6m, Δl=0.001m

ΔT= 0.02s

Experiment 3: Effects on angle, ϴ on time

ϴ| 10T(s)| 10T(Average)| T(s)|

5| 15.60| 15.80| 15.59| 15.68| 1.57|

10| 15.45| 15.60| 15.52| 15.52| 1.56|

30| 15.50| 15.44| 15.34| 15.45| 1.55|

50| 16.16| 16.19| 16.30| 16.22| 1.62|...

References: Investigation of a simple pendulum. 2004. http://www.practicalphysics.org/go/Experiment_969.html

(accessed 22 August 2011)

The Pendulum Eqaution. http://www.worsleyschool.net/science/files/pendulum/equation.html

(accessed on 21 August 2011).

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