To determine the acceleration of free fall (g) using a simple pendulum. To achieve this I must research background information provided in the specification.

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Chris Horswell                                                                      1st December 2002

Determine the Gravitational Field Strength (g)

at the Earths Surface, Using a Pendulum.

Aim: -

        To determine the acceleration of free fall (g) using a simple pendulum. To achieve this I must research background information provided in the specification.

        In my specification I am provided with the Periodic Time equation: -

L = Length - Measured in metres (m)

g = Gravity - Measured in Metres per second (ms  )

T = Periodic Time - Measured in second (s)

Background information

        “This was produced by Galileo in 1632. He was inspired by a swinging lamp, strung form the ceiling of the Cathedral in Pisa; using his pulse as a stopwatch, he calculated that the oscillations of the lamp remained constant even when the oscillations were dying away.” 

It was acting like a Pendulum.

A pendulum consists of a mass hanging from a string and fixed at a pivot point. Once released from an initial angle, the pendulum will swing back and forth with Periodic Motion.

  1. ‘a’ to ‘b’ to ‘c’ to ‘b’ to ‘a’ = 1 oscillation.
  1. at points ‘a’ and ‘c’ = greatest potential energy.
  1. at point ‘b’ = greatest kinetic energy.

This is a diagram showing the motions of the pendulum and forces acting on it. It shows where the bob passes once swinging and the Simple Harmonic Motion it follows. Also shown above is where the greatest potential and kinetic energy is. We shall refer back to this later in our preliminary work.

“Simple Harmonic motion is the movement of an object that moves with constant velocity back and forth with the same amplitude and period”

“Ordinary Physics” Page 183

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Simple harmonic motion is the vibrations of matter. Thus a important example of simple harmonic motion is the pendulum. In the picture on the left we can see the forces acting on the pendulum. By considering the motions of the pendulum, and Newton’s second law the moment of inertia is: -

and also the toque can be written as: -

The torque is negative, as it is acting in a motion to decrease the angle at which the pendulum was released from. Once simplified: -

This is the equation for simple harmonic ...

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