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In this laboratory report, we delve into the principles of Simple Harmonic Motion (SHM) through an experimental investigation involving a mass-spring system. The primary goal was to explore Hooke's law and SHM theory, applying different spring lengths and measurements to analyze the oscillation amplitude and period with the aid of LoggerPro software.
The objectiveaof this experimentais to investigateathe motionaof a mass on a springausing Hooke’salaw and the theoryaof simple harmonicamotion. This was done by usingadifferent lengthsaand measurements of the springain relationato the sensor and by usingaLoggerPro to collectadata on the amplitudeaandaperiod.
| Mass on Spring (kg) | Stretch of Spring (Δx) (m) |
|---|---|
| 0 | 0.758 ± 0.0005 |
| 0.05 | 0.752 ± 0.0005 |
| 0.10 | 0.705 ± 0.0005 |
| 0.15 | 0.656 ± 0.0005 |
| 0.20 | 0.608 ± 0.0005 |
| 0.25 | 0.560 ± 0.0005 |
| Mass (kg) | Height Raised (m) | Amplitude (m) ± 0.000005 | Period T (s) ± 0.005 | t₁ (s) |
|---|---|---|---|---|
| 0.2 | 0.05 | 0.07834 | 0.89 | 0.590 |
| 0.2 | 0.10 | 0.08122 | 0.92 | 0.373 |
| 0.3 | 0.05 | 0.09443 | 1.17 | 0.777 |
| 0.3 | 0.10 | 0.09469 | 1.11 | 0.890 |
The slope from the graph was determined as -0.0858 m/N.
Thus, the spring constant (k) is calculated as:
For a mass of 0.2 kg raised to a height of 0.05 m, the phase constant (Φ) was calculated using the formula:
Substituting the given values, we get:
For a mass of 0.2 kg, and angular frequency ω = 7.0597 rad/s, the spring constant (k) is calculated as:
m=0.2kg height=0.05m A=0.07834m
B=7.0597rad/s
C=0.674𝝅
A=0.07816m
B=6.871rad/s
C=0.665𝝅
m=0.2kg height=0.10m A=0.08122m
B=6.8295rad/s
C=0.595𝝅
A=0.08163m
B=6.879rad/s
C=0.178𝝅
m=0.3kg height=0.05m A=0.09443m
B=5.3702rad/s
C=0.336𝝅
A=0.04574m
B=6.670rad/s
C=1.634𝝅
m=0.3kg height=0.10m A=0.09469m
B=5.6605rad/s
C=0.198𝝅
A=0.09232m
B=5.669rad/s
C=1.383𝝅
ω = √ km
m 7.0597) (0.2) .968 N /mk = ω 2 = ( 2 = 9
The valueafor springaconstant calculatedapreviously was 11.66 N/m so it is fairly consistentabut has a 1.692 N/m differenceabetween the two valuesacalculated.
The experiment conducted provided insightful data on the behavior of a mass-spring system under simple harmonic motion.
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It was observed that the period of oscillation depends on the spring constant and the mass, but not on the amplitude. The phase constant and spring constant were calculated using the experimental data, which aligns closely with theoretical expectations, barring slight deviations attributed to experimental limitations like friction. The laboratory exercise reinforced the fundamental concepts of SHM and Hooke's law, enhancing our understanding of the dynamics of oscillatory systems.
Exploring Simple Harmonic Motion: An Experimental Investigation of a Mass-Spring System. (2024, Feb 18). Retrieved from https://studymoose.com/document/exploring-simple-harmonic-motion-an-experimental-investigation-of-a-mass-spring-system
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