LESSONS: Periodic Motion
The majority of lesson ideas below require minimal resources other than the smartphone, and are relevant to introductory physics in high school and college. However, creative individuals are using smartphone science in more complex ways, with drones, engineering kits, and much more. Follow us on Twitter @PhysicsToolbox and see our Publications page for additional content.
Pendula and Periods of Oscillation
What is the relationship between LENGTH, MASS, and PERIOD of a simple pendulum?
Try This
Using the Proximeter tool, measure the period of a simple pendulum constructed from a suspended string attached firmly to the mobile device. Use a meter stick to determine the relationship between pendulum length and period (if any). Use a balance to determine the relationship between the pendulum mass and period (if any).
Challenge Yourself

Create a graph of Period vs. Mass, and derive a mathematical expression for this relationship.

Create a graph of Period vs. Length, and derive a mathematical expression for this relationship.

If there are any constants in these mathematical expressions, explain their significance.

Does the angle of release have any impact on the pendulum? Explain how you know.
Related Resources

Eureka Magazine. "Obtaining Acceleration Due to Gravity with a Pendulum."

Mobile Science Wiki. "Measurement of Acceleration of Gravity and Angle of Release."

* Note: The lesson plan above refers to a "Mobile Science Pendulum" app, and is no longer available. However, this lab can be fully completed with Physics Toolbox Accelerometer alone and with or without any data analysis tool that can accept .csv files. Essentially, the app, developed by Forinash and Wisman, used Physics Toolbox Magnetometer to directly export data into a data analysis tool. Vieyra Software hopes to soon have direct data analysis capabilities in the future.*
Springs and Period of Oscillation
What is the relationship between MASS and PERIOD of an oscillating spring?
Try This
Using the Accelerometer tool, record the period of oscillation of your smartphone when attached to a vertical spring. Determine the graphical and mathematical relationship between mass and period of the spring. (If a spring is not available, a set of uniform rubber bands will suffice). Known masses can be attached to the mobile device, and additional objects can be massed using a balance. Determine the effect of using different uniforma sets of rubber bands.
Challenge Yourself

Create a graph of Period vs. Math, and derive a mathematical expression for this relationship.

If there are any constants in these mathematical expressions, explain their significance.

The "type" of spring affects the quantitive relationship of mass and period by a factor known as the "spring coefficient." Do thicker, stiffer rubber bands results in a higher or lower spring coefficient? Explain how you know.

Predict the unit(s) associated with the spring coefficient by doing unit analysis. Explain.
Related Resources

Mobile Science Wiki. "Harmonic Oscillation" video.

IoP Science. "Oscillations Studied with a Smartphone Ambient Light Sensor."
Spring Systems
What is the relationship between effective SPRING CONSTANT and SPRING SYSTEMS (series/parallel)?
Try This
Using the Accelerometer tool, record the period of oscillation of your smartphone when attached oscillating springs in a series or parallel configuration. Determine the effective spring constant in each scenario.
Related Resources
Inertial Balance
What is the relationship between MASS and PERIOD of an oscillating inertial balance?
Try This
Using the Accelerometer tool, measure the period of an oscillating inertial balance (either commercially obtained or fashioned out of two electrical boxes, metal strips, and screws) and masses.
Challenge Yourself

Create a graph of Period vs. Mass, and derive a mathematical expression for this relationship.
Related Resources

Asael BarreraGarrido. "A Smartphone Inertial Balance."
Potential and Kinetic Energy of a Pendulum
What is the relationship between POTENTIAL ENERGY and KINETIC ENERGY of a simple pendulum?
Try This
Using the Accelerometer tool, fix the smartphone to the end of a simple pendulum made from a string attached to a point. Before releasing the pendulum from a given height (measured from the bottom of the pendulum swing), determine the potential energy using the mass of the smartphone and a ruler. Release the smartphone. Using data from the acceleration when at the lowest point, determine the tangential velocity at the lowest point (and hence, the kinetic energy).
Challenge Yourself

How did the starting potential energy at the top of the swing compare to the kinetic energy at the bottom of the swing?

How would this relationship differ if potential energy had been measured from the ground, and not from the bottom of the pendulum swing? Why?

Draw energy pie charts for systems in which potential energy is measured from both frames of reference.
Related Resources
Gait Patterns
What is the relationship between the HEIGHT and GAIT FREQUENCY for walking humans?
Try This
Try This
Attach a mobile device to your back or chest area and collect data while walking using the gForce or Accelerometer tools. For various subjects, compare dynamic, gait, metrics, symmetry, and variability. Compare these traits in the data to physical characteristics, such as height or leg length. If desired, record video on another camera to compare data to visual observations.
Challenge Yourself

Create a graph of Gait Frequency vs. Height, and derive a mathematical expression for this relationship.

If there are any constants in these mathematical expressions, explain their significance.

Attach the mobile device to other parts of the body (thigh or leg). How does this data differ from that collected on your chest or back? Why?
Related Resources

Lesson Plan from Teach Engineering: "Identifying Gait Metrics." [External website]