THE SIMPLE PENDULUM

• General Background: A mass m hanging from a string whose length is L and a pivot point on which this mass is fixed are what a simple pendulum (which was discovered during the 10th century by Ibn Yusuf) consists of. During the 17th century, it is developed by some physicist, especially by Galileo.

When the mass hanging from the string is released with an initial angle, it starts to move with a periodic motion. The motion can be approximated as a simple harmonic motion if the pendulum swings through a small angle (so sin (ө) can be approximated as ө). The frequency and period for the simple pendulum are the independent of the initial angle of the movement (initial position of the mass to the vertical reference line). In addition to the initial angle of the mass, the period doesn’t depend on the mass of the object. However, it is affected by the length of the string which the mass is hanged on and the acceleration of gravity.

The most widespread applications of the simple pendulum are for timekeeping,

gravimetry (the existence of the variable g in the period equation of simple pendulum -

- means that the pendulum frequency is different at different places on

Earth), seismology, scholar tuning, and coupled pendula. It is also used for entertainment and religious practice.

• Aim: To determine the effects or contribution of the length of the string on the period for the simple pendulum and find out a mathematical relationship between the length and the period.

• Hypothesis: Since the length of the string which the mass is hanged on is shortened, the magnitude of the period for the simple pendulum gets increased. Different masses of the object hanging from the string have no effect on the period.

• Apparatus / Materials:

• A string used as a rigid rod

• A mass (pendulum)

• Table clamp

• A rod on which the mass is fixed

• Stopwatch

• Ruler

Figure 1: The Simple Pendulum

• Plan / Method:

1. Take a rod on which you will hang a mass on it and fix it on a linear surface by using table clamps. 2. Take an object which will be used as a mass for your pendulum and by using the top of the rod fixed on the table as a pivot point, hang the mass with a string (or rigid rod). .

Figure 2: Effects of angle on the frequency

and the period of the pendulum

3. Let the mass to start its periodic motion. Record the time taken by the motion of the pendulum to determine its period and repeat this step by taking the angle of the mass to the vertical reference line. 4. Change the mass hanged from the pivot point (without changing the length of the string, gravitational acceleration and the angle of the mass to the vertical reference line) and see whether or not it affects the period of the pendulum. Repeat this procedure for different masses and use 3 trials for each one. 5. Use the same masses and change the length of the string to observe either the mass of the length of the string (or both) affect the period of the movement. Repeat this procedure for different lengths of the string. Record your data on your data collection table.

p.c: Gravitational acceleration should be kept constant during the experiment.

• Variables:

1. Controlled & Independent Variables:

• Angle that the pendulum is released and weight, during examining the effects of length. • Length and angle, during examining the effects of weight. • Weight and the length of the pendulum, during examining the effects of angle

2. Dependent Variables:

• Period for the simple pendulum

Figure 3: Effect of the length of the string on the period for the simple pendulum.

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Potential energy and phase portrait of a simple pendulum. [[1]]...