SHM: determining acceleration due to gravity

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Student Name: WONG Wing Yan

Class and class no. : 6G2 (22)

Date of experiment: 25th March, 2009

Experiment 5 – SHM: determining acceleration due to gravity

Objective

In this experiment, we are going to study the simple harmonic motion of a simple pendulum. The acceleration due to gravity (g) can be estimated by the following set-up.

Apparatus

 

Setup


Theory

A simple pendulum can perform a simple harmonic motion as shown in figure 2. The acceleration due to gravity can be determined if we know the period (T) of the SHM and the length of the string ().

        A light string with its upper end fixed and lower end attached to a pendulum bob mass m is shown. When the string is held to make and angle  with the vertical, the bob displaces an arc length . The restorting force acting perpendicular to the bob is

If the bob is released, it will move with an acceleration (a) towards the equilibrium position O. By Netwon’s second law of motion, we have:

For small angle (e.g. < 10), we have sin  and therefore sin. Hence, it becomes:

As the bob continues to move, it performs a simple harmonic motion with angular velocity () and it has an acceleration (). By comparing it with the equation, we have:

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However, the period can be shown as follows:

Note that period of the simple harmonic motion is independent of the mass.

Procedure

  1. The apparatus was set up as shown in Figure 1.
  2. The bob was moved to a height so that the attached string was taut and an angle of 10 was made with the vertical.
  3. The period (t1) for 20 complete oscillations was measured and it was recorded in the following table.
  4. Steps 2 and 3 were repeated for another measurement of period (t2).
  5. ...

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