Unit 3 - Oscillation

Lab 3A: Vertical Mass-Spring

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University of California, Los Angeles

Department of Physics and Astronomy

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Physics 4AL

Outline of Lab 3A

• 3A In-Lab
• Hooke’s Law measurement of spring constant
• Harmonic Oscillations using Arduino

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Hooke’s Law

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Hooke’s Law

• Find the spring constant of the spring.
• Fix the spring to the small rod on the stand and hang masses from the springs and note the displacement using a ruler.
• You can combine masses by using the hooks at the ends. You can use the weighing scale to find the mass values.

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TA Checkpoint 1 - Hooke’s law Plot

• Plot position (y-axis) vs mass (x-axis) along with the best fit line
• Determine Spring constant (k = g / slope) with uncertainty using polyfit and covariance
• Recall for uncertainty you will have to propagate the reciprocal of slope (as for Speed of Sound in Pre-Lab Week 3)

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Harmonic Oscillations

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Wireless transmission of data

• Use the multimeter to check the voltage of the batteries that you will be using.
• If the voltages are greater than 1.37 V then use these batteries in the battery holder to power your setup.
• If the voltages are lower than 1.37 V then use a different set of batteries.
• Connect the ultrasound and bluetooth modules to your arduino setup.
• Verify if your arduino setup with ultrasound, accelerometer and bluetooth is able to send meaningful data to the Arduino IDE wirelessly
• The ultrasound will be the first sensor to provide meaningless values at low voltages.

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Arduino setup as mass in mass-spring system

• We will be working with only one member’s setup.
• Before taping the battery holder to the Arduino setup, guide a thread through the 2 holes in the Arduino and the 2 holes in the prototyping shield
• Make sure that your string is long enough to hang your Arduino from a spring and get clean data

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Calibration x axis

• Before the setup experiences oscillations, we will need to re-calibrate the accelerometer in the axis of oscillations.
• Before mounting the setup on string, we need to rest the accelerometer on a table to find the calibration in the x-direction.
• Follow the steps mentioned in Lab 2D to calibrate your accelerometer in x-direction.
• Collect >= 20 data points (each orientation)

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Relative Acceleration from Calibration Constants

• Now you can find acceleration in m/s² using calibration constants:

Total acceleration = slope*analog_output + intercept

• You can create a function to automate the task to find the relative acceleration!
• We want to nullify the effect of the smaller mass experiencing acceleration of g in static conditions

Relative acceleration = Total acceleration - Acceleration due to gravity (g)

Recall g is defined as -9.81 m/s² so subtracting by -9.81 is equivalent to adding +9.81

You will essentially zero out the effect of gravity

(your relative acceleration will equal 0 m/s² when only gravity is acting)

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• You will plug in your analog_output data for this oscillations experiment to determine the relative acceleration of your hanging mass

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Spring mass system

• Tape the battery holder to the setup now so that you have one compact unit
• Knot the ends of the thread so that you have the ultrasound facing downwards (to the best of your ability)
• Weigh your Arduino setup (with the battery holder)
• Balance your setup at one end of the spring
• Make sure that the ultrasound will reflect off the ground and not any other part of the stand

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Spring

Thread

Arduino setup

Stand

Harmonic Oscillations (TA Checkpoint 2)

• Pull the mass slightly down and let go for the system to oscillate.
• Collect data for 15 cycles.
• Import the data into Python and plot the ultrasound data (distance in m) vs elapsed time.
• Using your calibration function, plot final array (relative acceleration in m/s²) vs elapsed time

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Relative acceleration should be centered close to 0 m/s^2

Post-Lab Requirements for lab 3A

• Plot the displacement vs. mass of the mass-spring system. Include axis labels, title, units, best-fit line

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• Calculate the spring constant of your spring, including uncertainty and units. Also record the mass of your Arduino setup here

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• Include your plot of distance vs. time oscillations obtained from the bouncing Arduino’s ultrasonic sensor. Include title, axis labels, units

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• Include your plot of relative acceleration vs. time oscillations obtained from the bouncing Arduino’s accelerometer. Include title, axis labels, units