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The Simple Pendulum

- Recall from lecture that a pendulum will execute

simple harmonic motion for small amplitude

vibrations. - Period (T) - time to make one oscillation
- Frequency (f) - number of oscillations per unit

time

Frequency

Period

In symbolic form

or

- The period is independent of the mass of the

pendulum. - The period depends on the length of pendulum.
- It also depends on the amplitude (angle of

swing).

- If the displacement angle is small (less than

100),

- then the period of the pendulum depends primarily

on the length (l ) and acceleration of gravity

(g) as follows.

It must be emphasized again that this equation is

good for small angles of vibration but not for

large.

- Squaring both sides of the equation yields

- Lets rewrite this equation to get

- This is of the form (from last weeks lab)

T 2 is y 4p 2/g is m l is x and b will equal

zero

- Therefore by plotting T 2 versus l and using the

slope of this curve one can determine the

acceleration due to gravity g. The slope is

- Multiply both sides of the equation by g and get

This reduces to Now divide both sides by the

slope to get which reduces to

Purpose of Todays Experiment

- You will determine the local value of the

acceleration due to gravity by studying the

motion of a simple pendulum. - Note Pendulums are used in a variety of

applications from timing devices like clocks and

metronomes to oil prospecting devices.

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