PHY211Lab_Week13_Pre-Lab

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Apr 3, 2024

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PHY211LB (Summer 2021) Pre-Lab The Simple Pendulum (Lab Week 13) Name: Two different views of a simple pendulum (of length ) are shown below. Both views show a single period of motion with the mass ( ) traveling from the right side of the pendulum to the left side and then back again to the right side. The left-hand picture shows images captured in time and superimposed together. The right-hand picture shows the corresponding individual images in time, moving from left to right. The angle is positive when the pendulum is to the right and negative when it is to the left. The angle at two instances when the pendulum is perfectly vertical. 1. The angle from the same pendulum may be plotted as a function of time, as shown in the figure below. Several specific times are identified on the time-axis and these are labeled A through F . The period (given the symbol ) is discussed in section 5.13 of your lab manual and in section 14.1 of the textbook. Using the figure above, with the times marked A F , specify two letters (as a range) that would describe one period.
Period is related to frequency ( ) and angular frequency ( ) as follows (see section 14.1 of your textbook): . Units for each of these quantities are shown in parenthesis. Frequency has units of hertz, where The symbol for angular frequency is the Greek letter omega (so , those are two different letters). 2. Fill in the table below. Start by converting degrees to radians, reporting your answers with four significant figures. Then calculate (also with four significant figures). Finally, using your values for in radians and your values for , determine the percent difference between them. (degrees) (radians) 45.00 30.00 15.00 5.000 So, as gets smaller, you can use the approximation (as long as you use radians for the angle). 3. In section 5.13 of the lab manual you will make use of the equation . This equation relates the period to the pendulum length in a power-law relationship. Section 5.13 also reviews the procedure for taking a power-law equation and transforming it to a linear equation using logarithms. Using this procedure, show how you would obtain the equation from the equation . (Show all of your work.)
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