Simple Harmonic Motoion - Lab Report Example

Simple Harmonic Motion Objectives of the experiment. The main objectives of this experiment include: To construct simple pendulums, and find their periods.To generate values for (Ag) the free fall acceleration.To evaluate the relationships between length and period for different pendulums.Introduction.Simple harmonic motion involves an oscillating motion where by the restoring force is proportional to the displacement. When a system is set in a to and fro motion, a periodic motion is produced.

This is referred to as vibration. When a body is at rest, it is said to be at its equilibrium position. For any vibration to occur, a restoring force must be in existence. In this respect, a restoring force is identified in a pendulum. The restoring force is applied by the springs as long as Hooke’s law is observed. The restoring force, therefore, is proportional to the extension (e) with the constant (K) as the spring constant. That is force is equal to the extension times the spring constant (f=k e).

The number of oscillations per unit time is equal to the frequency. Frequency is measured in units referred to as hertz (Hz). The motion of a simple pendulum is one of the phenomena that can be used to approximate the simple harmonic motion. The motion is sinusoidal and is a demonstration of resonant frequency that is single (Dunwoody 10). A pendulum is a simple set up in which a string is attached to a small bob. The string is clamped, and when it is displaced, it swings in a to and fro motion.

The time that would be taken to complete one oscillation is referred to as periodic time (T). The periodic time depends on the length of the pendulum and the acceleration due to gravity (g). That isT=2π√ (l/g) Where l is the length of the pendulum whereas g is the acceleration due to gravity (g).When a body is vibrating, its potential energy is converted to kinetic energy (Dunwoody 13). Studies advanced on a simple pendulum reports that the period value depends on its length. Another study argues out that the important property of a pendulum which makes be used in timekeeping (isochronism) (Dunwoody 15).

This study identified the period as the pendulum’s prime property and that it depends on the square root of the pendulum’s length. This paper explores an experiment of simple harmonic motion by studying a pendulum. The hypothesis of this experiment is that increasing the length of the pendulum shall increase the periodic time (T) of a simple pendulum.Apparatus to be used for the experiment.A simple pendulum,Stop watch,Metre rule, And protractor.Procedure.The simple pendulum was set up. The set up was made up of three regions.

The centre was the pendulum. The length of the pendulum was chosen for the pendulum by using the slider on the left side of the screen. This value was recorded in the data table. The amplitude was raised to about 20 degrees. This value was equally recorded in the data table. The start animation button was clicked, and when the pendulum passed its lowest point, the timer was started. The time taken for the pendulum to complete 10 cycles was taken, and the timer stopped as the pendulum passed through the lowest point once again.

This time was recorded in the data table. The mass of bob and the amplitude were kept constant. The length of the pendulum was varied and the period of oscillation determined for certain pendulum length. A series of the values for the period were determined through a number of trials. The length of the pendulum was varied so as to determine whether the period of oscillation depends on the length of the pendulum cord. Four more trials were done using the same amplitude but changing the pendulum lengths.

The results obtained were used to plot a graph of period versus the length and graph of period against the square root of the length. Results.Table 1: A table showing the data collected.TrialLength (m)L2 (m2)Time for 10 oscillation (s)S2 (sec2)Period (seconds)Ag 1st0.100.016.7500.45590.6758.662nd0.150.02258.1400.66240.8148.943rd0.200.0409.2600.85820.9269.204th0.250.062510.261.0521.0269.38T=2πAg = A graph of Period against length of the pendulum.A graph of period against the square root of the length .

First Trial.Absolute error = ׀experimental – accepted׀Where the accepted Ag value is 9.81m/s2Absolute error = ׀8.66-9.81׀= 1.15Relative error =׀ experimental – accepted׀ /accepted= Absolute error/ accepted1.15/9.81= 0.1172Trial 2Absolute error = ׀ 8.94- 9.81׀ =0. 87 Relative error = 0.87/9.81= 0.08868Trial 3Absolute error = ׀9.20 – 9.81׀ = 0.61Relative error = 0.61/9.81= 0.06218Trial 4Absolute error = ׀9.38 – 9.81׀ = 0.43Relative error = 0.43/9.81= 0.04383Conclusion.From the data collected, the graph of period versus length is a straight graph.

This shows that as the length of the pendulum increases, the period of the oscillations increases too. As the length of the pendulum increases, the periodic time increases and as the length of the pendulum decreases the periodic time of the pendulum decreases. From the experiment, it was also evident that the periodic time does not depend on the mass and the amplitude of oscillation. This is supported by a prior practical that was advanced in this topic (Dunwoody 10). This practical reported that the length and the gravity pull on the pendulum were two factors that affect the oscillations of a pendulum (Dunwoody 10).

For a small-angle approximation, the simple pendulum motion is approximated by use of the simple harmonic motion. The results of this experiment are also supported by the evidences that a pendulum of a fixed length would swing more slowly on the moon due to the moon’s low gravitational acceleration. This, therefore, approves the hypothesis for this experiment.Possible sources of error.Absolute error is an error due to the measurements of the length of the pendulum. For the case of the pendulum, the errors occurred due to parallax in taking reading.

Some faultiness in the stop watch could also lead to absolute errors. Relative error, on the other hand, represents the error ratio to the absolute error value to the accepted value. In this experiment, these errors occurred due to the inaccurate timing, and due to the air resistance that causes a change in the oscillation during the experiment. These errors can, however, be minimised by avoiding parallax while taking the reading and minimising the air resistance during the experiment.Work citedDunwoody, Halsey.

Note, Exercise, and Laboratory in a simple pendulum. New York: John Wiley & Sons.2000.