Equations of Motion - Essay Example

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, H. 2000). 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 is T=2?v (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, H. 2000). . This paper explores an experiment of simple harmonic motion by studying a pendulum (Grant, R., 2005). The hypothesis of this experiment is that increasing the length of the pendulum shall increase the periodic time (T) of a simple pendulum. Method Apparatus The instruments and apparatus that were used in this experiment included the simple pendulum, stop watch, meter rule, and protractor.

Procedure. The simple pendulum was set up. The setup 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. About four 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. Trial Length (m) L2 (m2) Time for 10 oscillations (s) S2