PHYS 2111 - Expt 9 Simple Pendulum

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Oct 30, 2023

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The Simple Pendulum Objective: • To learn the definitions of period and frequency, and the relationship between them • To find the relationship between the length of a simple pendulum and the period of oscillation • To measure g with the simple pendulum • To study the amplitude and mass dependence of the period of a pendulum Introduction: Many things in nature vibrate n a periodic fashion. One such example is a simple pendulum. If we suspend a mass at the end of a piece of string, we have a simple pendulum. The to and fro motion represents a periodic motion used in times past to control the motion of grandfather and cuckoo clocks. Such oscillatory motion is called simple harmonic motion . It was Galileo who first observed that the time a pendulum takes to swing back and forth through small distances depends only on the length of the pendulum . The story goes that Galileo was in church one day when he found his attention diverted from the Mass to the regular swaying of a lantern. Using his pulse as a crude watch, he observed that the period of the motion was independent of its amplitude, an observation which he later sought to confirm with greater precision using a water clock. This discovery led to our understanding of pendulums. A simple pendulum consists of a mass called the pendulum bob, hanging by a cord from a rigid support. Pendulums have been used as the regulating mechanism in clocks for hundreds of years. Pendulum motion was first investigated scientifically by Galileo and Foucault later used a pendulum to demonstrate the rotation of the Earth. In this experiment you will investigate how the period of a pendulum depends on its length and the mass of the bob. A few definitions • The period of a pendulum is the time required for one complete swing to and fro. • The frequency of a pendulum is the number of complete swings in one second. From these definitions; Frequency=1/period
According to our textbook, the period of a simple pendulum is proportional to the square root of length as shown with the relation; 𝜏 = 2𝜋√ 𝐿 ? Which can also be written as: 𝜏 2 = 4𝜋 2 ? 𝐿 Experiment 1. Copy and paste the link below and paste it in a browser https://phet.colorado.edu/sims/html/pendulum-lab/latest/pendulum-lab_en.html 2. Of the three options, double click on “Intro” Activity I 3. On the top right tub, adjust “Length 1” to 0.4 m 4. In the same tub, adjust the mass to 0.5 kg 5. On the Gravity tub, ensure it reads “Earth” and the “Friction” is set on zero 6. On the button menu, click on the circle next to “slow” to activate it. 7. On the bottom left corner, click on the box next to the stop watch to activate the stop watch 8. Take a screenshot of the page to show all the settings and put it in your report. 9. Click and drag the mass to the right so the angle reads any number between 2 o and 5 o [Note – If you accidentally release the mass, you can click on the red stop sign and try again] and release it 10. Record the angle you used here and use it for the rest of activity I
11. Click on the start button on the stopwatch and use it to time for 20 oscillations [one oscillation is when the mass starts from the right side, swings to the left and back again] 12. Create a table like the one below for all your measurements and calculations Length (m) Time for 20 oscillations Period τ (s) τ 2 (s 2 ) 𝑃??𝑖?? 𝜏 = ?𝑖?? ?????? ?? ???𝑖????𝑖??? 13. Change the length to 0,5 m and move the mass to the right (the same angle you used for the 0.4 m) and release it. Record the time for 20 oscillations. 14. Repeat step 13 for 0.6 m, 0.7, 0.8, 0.9 and 1.0 m 15. Complete the table with the lengths and the appropriate calculations 16. Plot a graph of 𝜏 2 on the vertical axis and length on the horizontal axis 17. Find the slope of the graph 18. From the slope, find the acceleration due to gravity 19. Calculate the percentage error Activity II 1. Click on the icon on the bottom right corner to reset the screen 2. On the Gravity tub, change from Earth to Jupiter
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3. Repeat steps 3 to 19 of activity I Q1. How does the gravity values from the two activities compare? Q2. Would a change in mass of the pendulum affect the period of the pendulum? Explain. Activity III 1. Click on the icon on the bottom right corner to reset the screen 2. On the Gravity tub, ensure it reads “Earth” and the “Friction” is set on zero 3. On the button menu, click on the circle next to “slow” to activate it. 4. On the bottom left corner, click on the box next to the stop watch to activate the stop watch 5. Take a screenshot of the page to show all the settings and put it in your report. 6. Click and drag the mass to the right so the angle reads 2 o [Note – If you accidentally release the mass, you can click on the red stop sign and try again] and release it 7. Click on the start button on the stopwatch and use it to time for 10 oscillations [one oscillation is when the mass starts from the right side, swings to the left and back again] 8. Create a table like the one below for all your measurements and calculations Angle time Period for 10 oscillations
9. Repeat steps 6 & 7 for angles s3, 4,5,6,7,8,9,10,12,14,16,18,20,22,24,26,28 and 30 degrees. 10. Plot a graph of period on the vertical axis and angle on the horizontal axis Q. How does the angle affect the period of oscillation

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