SHM-1 - Simple Harmonic Motion PART I: POSITION AND...

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Simple Harmonic Motion PART I: POSITION AND VELOCITY IN SHM Lots of things vibrate or oscillate. A vibrating tuning fork, a moving child’s playground swing, and the loudspeaker in a radio are all examples of physical vibrations. There are also electrical and acoustical vibrations, such as radio signals and the sound you get when blowing across the top of an open bottle. One simple system that vibrates is a mass hanging from a spring. The force applied to the hanging mass by an ideal spring is proportional to how much the spring is stretched or compressed. Given this force behavior, the up and down motion of the mass is called simple harmonic and its position can be modeled with y = A sin 2 π ft + φ ( ) In this equation, y is the vertical displacement from the equilibrium position, A is the amplitude of the motion, f is the frequency of the oscillation , t is the time, and is a phase constant. This experiment will clarify each of these terms. Figure 1 OBJECTIVES Measure the position and velocity as a function of time for an oscillating mass and spring system. Compare the observed motion of a mass and spring system to a mathematical model of simple harmonic motion. Determine the amplitude, period, and phase constant of the observed simple harmonic motion. MATERIALS computer ring stand, rod, and clamp Vernier computer interface Logger Pro Vernier Motion Detector spring, with a spring constant of approximately 10 N/m 200 g and 300 g masses twist ties
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PRELIMINARY QUESTIONS 1. Attach the 200 g mass to the spring and hold the free end of the spring in your hand, so the mass and spring hang down with the mass at rest. Lift the mass about 10 cm and release. Observe the motion. Sketch a graph of position vs . time for the mass. 2. Just below the graph of position vs . time, and using the same length time scale, sketch a graph of velocity vs . time for the mass. PROCEDURE 1. Attach the spring to a horizontal rod connected to the vertical stand and hang the mass from the spring as shown in Figure 1. Securely fasten the 200 g mass to the spring and the spring to the rod, using twist ties so the mass cannot fall. 2. Connect the Motion Detector to the DIG/SONIC 1 channel of the interface. If the Motion Detector has a switch, set it to Normal. 3. Place the Motion Detector at least 75 cm below the mass. Make sure there are no objects near the path between the detector and mass, such as a table edge. 4. Open the file “15 Simple Harmonic Motion” from the Physics with Vernier folder. 5. Make a preliminary run to make sure things are set up correctly. Lift the mass upward a few centimeters and release. The mass should oscillate along a vertical line only. Click to begin data collection. 6. After 10 s, data collection will stop. The position graph should show a clean sinusoidal curve. If
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SHM-1 - Simple Harmonic Motion PART I: POSITION AND...

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