Lab 07_SImple Harmonic Motion

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Faith Mackey December 5 2022 PHY 121 L69 Jae Sung Lee Simple Harmonic
Introduction: The purpose of this lab is to experimentally calculate the angular frequency given its theoretical value using simple harmonic motion. Relationships between the mass and angular frequency will be observed in object oscillation. Simple Harmonic Motion records the physical properties of oscillatory motion in relation to mass, acceleration, distance, and restoring force. Newton’s Second Law, F(net)=ma, can be transformed into another equation, where w=(k/m)^-.5 to explain how an object in oscillation. My hypothesis for this experiment should conclude that the displacement of the mass from the starting position is inversely proportional to the angular frequency. Procedure: Part I- Find Mass 1. Attach force probe to device 2. Record device at rest position, y-axis downward 3. Pick up device and hold in air 4. Place device down and end the recording 5. Find mass using Fg/Ag=mass(kg) Part II 1. Attach long spring to device 2. Attach another end to a paper clip 3. Oscillate the device up and down the y-direction 4. Record restoring force 5. Record time between 5 peaks 6. Record frequency peak at 4096 7. Plot values
Part III 1. Repeat Part I and Part II using a second mass 2. Plot values Part IV 1. Repeat Part I and Part II using a third mass 2. Plot values Results : Figure (01) represents the gravitational force and acceleration of the IO device
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Figure (02) represents the gravitational force and acceleration of the IO device+m1 Figure (03) represents the gravitational force and acceleration of the IO device+m1+m2 Mass (kg) Angular Frequency 0.667 8.225 0.69 7.814 0.85 7.09 2.347 1.221 1.124 FFT (Hz)
Figure (04) represents the inversely proportional relationship between mass and angular frequency. Figure (05) represents the inversely proportional relationship between mass and angular frequency Significant Findings - Mass and Angular Frequency are inversely proportional - The B value is -0.561 - The A value is 6.46 Calculations: Error Analysis
Mass of IOB device
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Mass of IOB device + mass 1
Mass of IO device + m1 + m2
Discussion: In this discussion, it can be shown that t he angular frequency is expressed in the equation as w=Sq root (k/m) and A is (sq root k) and B is -0.5. The experimental equation represented in my plot supports my hypothesis. As the mass increases, the angular frequency decreases. The observed B value is extremely close to the expected B value. The given spring constant value is measured to be 11.5, and its square root is 3.39. Also, m y calculated A value is almost twice this value. However, The experimental angular frequency values displayed in (figure 04) are close in value because the period values of each trial are very similar. But, he system with the heavier mass has a much longer period compared to the system with the lightest mass. This margin of error can be observed through an experimental error when calculating the mass and instrument error analysis. To concur, this is way to make progress in the experimental precision is through repetition. Proof:
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