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Lab 6-Pendulum motion. Driven Oscillations. Resonance. Q

# Lab 6-Pendulum motion. Driven Oscillations. Resonance. Q -...

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Pendulum motion. Driven Oscillations. Resonance. Q Experiment #6 May 29, 2007 Section 3 Lab Station 9 Introduction:

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The purpose of this experiment is to investigate the motion of a swinging pendulum that is underdamped, critically damped, and overdamped. In the first part of the experiment, we study the damping affects on a pendulum. We do this by using a magnet to slowly lessen the amplitude of the system. Using a pendulum allows us more of a damping force to be applied to the pendulum. We used a rotary sensor to record all of this data. In the second part of the experiment, we are able to see the driven oscillations and the resonance experienced by the system. By using a spring connected to the system, we are able to simulate driven oscillations and observe the system at different frequencies which eventually allows us to find the resonance frequency. This resonance frequency allows us to determine the maximum amplitude. Equations: Equation of Motion for Pendulum: Ix bx Mgl =- - Torque from eddy current on blade: b - Torque due to gravitational force on center of mass: s Mgl - Torque applied by small spring: B - Simple Harmonic Equation of Motion: ( Ix kx =- =- Moment of Inertia (1): 2 1 1 1 3 M d I x Moment of Inertia (2): 2 2 2 I M I x Total Moment of Inertia: 1 I I = Length from pivot to center of mass: ( 29 1 1 2 2 M l M l l M + Frequency of Simple Harmonic Motion: ( 29 free Mgl B k I I ϖ + = = Equation for Quality Factor (Q): ln( _ ) 2 average pk pk Q π - - = “Frequency Scan” Quality Factor: resonance fs f Q f = Calculating the Phase: 1 2 2 (tan ) cot 2 y yl φ = = Procedure: Part 1. To perform the first part of this experiment, we first measure the dimensions of the pendulum. Following this, we set up the photogate so that the pendulum blade just unblocks it when it begins to swing back and forth. We make sure that the photogate is kept at a predetermined location in order to ensure that there are no discrepancies in the data which is collected by the computer program. After these two items are properly set up, we pull the
pendulum back the same angle for every run. The first run is performed without any damping or presence of the magnetic gap. After this, the same procedure is repeated using the magnets placed at 70 mm, 50 mm, 40 mm, 30 mm, 20 mm, 15 mm, 10 mm, and 5 mm respectively. Once we perform all of these runs, we can plot it on a graph and visually see the damping occurring in the system and how the amplitude decreases with a greater rate as the distance of the magnet gap diminishes. Using this data, we are also able to determine the point at which the magnet gap causes critical damping in the system. Part 2. To perform the second part of the experiment, we set up the equipment just as we did in the first part, but this time we do not need the photogate at all. In order to produce a driven oscillation, a spring is attached to the top of the pendulum. We then control the amplitude of the system using the computer program and this causes the pendulum to oscillate at a consistent rate. We then vary the drive frequency of the system to document any changes that may occur. This

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Lab 6-Pendulum motion. Driven Oscillations. Resonance. Q -...

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