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Physics 4AL Lab 4 - 2019 Summer Session A

Two masses three springs system

  • Nhu Dang - Biochemistry
    • Data Recording
    • Data Fitting of Left Mass
  • Jessie Mao - High School
    • Hardware Construction
    • Data Recording
  • Henry Ma - Physics
    • Data Analysis
    • Data Fitting of Right Mass

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Overview and Objectives

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Experiment 1

One mass, two springs

Experiment 2

Two masses, three springs

Objective 1

Confirm relationship between x(t) and a(t) by fitting data.

Objective 2

Compare theoretical and experimental ω’s

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Theory

Experiment 1

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Experiment 2

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~Antisymmetric:

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~Symmetric:

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Conceptual Drawing

Experiment 1

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Experiment 2

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diagram for single antisymmetric

  1. Parallel-Sym b) Parallel-Antisym

diagram for parallel antisymmetric

  1. Single-Sym b) Single-Antisym

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Video

Single-Symmetric

Single-Antisymmetric

(https://drive.google.com/file/d/1NbHuMusBIXqHZLbxqMj7KjkLVv6JzigO/view?usp=sharing)

(https://drive.google.com/file/d/1oVYZzZbHYFcntZLt4BZRDpMWNsQpOco7/view?usp=sharing)

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Data Taking and Analysis

Data Recording

  1. Accelerometer --- a(t)
  2. Ultrasound --- x(t)

Data Analyses

  1. Best fit curve
  • Wifi chip
  • connect to computer
  1. Extract best ω
  2. Derivatives of fitted x(t) to compare with a(t)

pictrure of python code

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Results (Experiment 1)

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Results (Experiment 2)

left

right

left

right

Single symmetric

Single antisymmetric

fit a(t)

experimental a(t)

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Results (Experiment 2/ω’s)

Experiment 1

Experiment 2

Experimental

ω

Theoretical

ω

4.155

4.069

2.935

2.877

5.841

5.754

4.625

4.549

3.647

3.524

5.094

4.983

2 single

2 series

2 parallel

series + parallel

series + single

parallel + single

Experimental

ω

Theoretical

ω

3.146 (L)

3.115 (R)

2.852

5.079 (L)

5.075 (R)

4.940

3.132 (L)

3.064 (R)

2.852

6.251 (L)

6.320 (R)

6.378

single symmetric

single antisymmetric

parallel symmetric

parallel antisymmetric

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Conclusion/Future Direction

Conclusion

  • Need better WiFi chip

Future direction

  • Get less noisy data to do a(t) —>x(t) analysis both directions
  • Do a mixed symmetric or antisymmetric oscillation next
    • decompose it into normal modes
    • Energy transf er between masses

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