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## The Simple Pendulum

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**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**Period**Frequency**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 the acceleration due to 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**• Let’s rewrite this equation to get**This is of the form (from last week’s lab)**T 2 is y 4p 2/g is m lis 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 Today’s 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.