University Physics II Experiment 2: Simple Harmonic Motion Objective: (1) To study the motion of a simple pendulum, the period of its oscillation in terms of the pendulum's length and the acceleration due to gravity; (2) to study the vertical motion of the spring-mass system and calculate the spring constant. Background & Equations: A simple pendulum consists of a mass attached to a very light string of some length L, hung from a fixture. Once set in motion, the pendulum will oscillate, and one complete cycle of its oscillation is its period T. The period of oscillation depends on the length of the pendulum and the acceleration due to gravity. Ttheoretical = 2n (eq. 1) Frequency and period can be related by eq. 2. Frequency gives the number of oscillations in a given time unit. f= = (eq. 2) Equipment: 1. Pendulum Consisting of: a. Light-weight string or durable sewing thread b. Metal screws or washers c. Pencil to tape to your desk, or two chairs with a rod (broom or mop rod) resting on top of the back supports. 2. Carpenter's tape measure 3. Protractor Sample equipment set up: 10 inchesProcedure: Part 1: Changing the length: 1. Construct a simple pendulum starting with 20 cm length. 2. Hang the pendulum as pictures in one of the two methods shown above. 3. Using the protractor, displace the pendulum 10 degrees from the vertical. 4. Release the pendulum and using a stopwatch measure the time for 5 complete cycles. 5. Repeat the procedure for the remaining lengths in the table. 6. Complete all calculations and discuss your results. 7. Make a graph of Tz vs. L. What does the slope represent? Discuss the graph. 8. How does changing the length affect the period of oscillation? Would changing the mass affect the period? Length (m) Time for 5 Frequency, f cycles (s) Period, T (s) Experimental (1/s T2 (s ? ) 0.2 0.3 0.4 D.5 0.6 D.7 D.8 0.9 10 Average experimental Accepted g: 9.8m/s2 Average experimental g ( from data table): % error: Experimental g (from graph's slope): % error:Part 2: Changing the amplitude: 1. Use the pendulum with a length of 100 cm (1 m) using the same set up as in Part 1. 2. Using the protractor, displace the pendulum 20 degrees from the vertical. 3. Release the pendulum and using a stopwatch measure the time for 10 complete cycles. 4. Repeat the procedure for the remaining angular displacements in the table. 5. Calculate the period for each angular displacement. 6. Discuss your observations. How does changing the amplitude affect the period? Angular amplitude Time for 10 cycles (s) Period, T (s) 205 30 609 Part 3: Changing the mass: 1. Use the pendulum with a length of 100 cm (1 m) using the same set up as in the previous parts. 2. Using the protractor, displace the pendulum 20 degrees from the vertical. 3. Release the pendulum and using a stopwatch measure the time for 10 complete cycles. 4. Repeat the procedure increasing the mass of the pendulum. You can attach more metal objects to your existing mass, or simply change the mass for a different, heavier object. 5. Calculate the period for each mass. 6. Discuss your observations. How does changing the mass affect the period? Mass Time for 10 cycles (s) Period, T (s) Original mass Increased mass 1 Increased mass 2 Increased mass 3