Waves and Simple Harmonic Motion

In this investigation we study a slowly varying sine wave signal produced by a function generator and amplified by a power amplifier to light a small #50 lamp.  We are specifically interested in seeing the relationship between the light intensity of the lamp and the current it is carrying at any given instant of time.  PocketLab Voyager is a perfect laboratory for performing this investigation even though Voyager does not have a current sensor.

A classic way to demonstrate the wave nature of light is to pass a coherent beam of light from a laser through a double slit.  In this lesson, students study the intensity of light in the resultant interference pattern using the light intensity sensor of PocketLab Voyager.  Students also compare intensity to theoretical predictions.  In addition, the wavelength of the light can be calculated from knowledge of slit separation, distances between bright fringes in the interference pattern, and distance from the double slit to the pattern. 

One of the most well-known physical laws related to polarization is Malus’s Law.  This law states that the intensity of plane-polarized light passing through a rotatable polarizer analyzer varies as the square of the cosine of the angle through which the analyzer is rotated from the position giving maximum intensity.  The lesson described here allows you to verify Malus’s Law using PocketLab Voyager and one of the light polarizers contained in the PocketLab Scientist Kit.

Virtually every student of physics has done an experiment to verify the inverse square law of light—light intensity is inversely proportional to the square of the distance from the source of the light.  With PocketLab Voyager this is a quick and easy experiment that is also a lot of fun to perform!

This experiment allows one to do a quantitative investigation of the damped harmonic motion of a swinging pendulum.  The pendulum is a piece of wood about a yard long from a Michael's hobby shop one end of which has been attached to a PocketLab by a rubber band.  The other end is taped to the top of a doorway, allowing the resultant pendulum to swing back-and-forth as shown in the image below.

An oscillating cart with a PocketLab provides an interesting way to study Newton's Second Law of Motion as well as some principles of damped harmonic motion.  The apparatus setup is shown in the figure below.  The small dynamics cart that can quickly be made from parts included in the PocketLab Maker Kit is shown in its equilibrium position.  Rubber bands are attached to each side of the cart and to two ring stands weighted down with some heavy books.  It is best to use rubber bands that provide as small Newton/meter as possible.  PocketLab is attached to the cart with its x-axis parallel t

PocketLab is a perfect device for determining the quantitative relationship between the length of a pendulum and its period of oscillation.  Pendulums of known lengths were made from balsa wood strips such as those available from Michaels and other hobby stores.  The photo below shows six such pendulums of lengths 15, 30, 45, 60, 75, and 90 cm alongside a meter stick.  The picture shows that PocketLab was taped with double-stick mounting tape to the pendulum whose length is 45 cm.

This investigation shows how VelocityLab allows for a quick and easy demonstration of damped harmonic motion.  The photo below shows the experiment setup as performed by the author.  A jellied cranberry sauce can was selected as there is virtually no sloshing of the cranberry sauce as the can oscillates back-and-forth on a curved piece of laminate flooring.  The center of the flooring is clamped down to the table with an adjustable wrench.  The ends of the laminate flooring are raised a little with some small wood blocks.  The cranberry sauce can is shown at rest at the VelocityLab zero pos

Exploration

Explore principles of harmonic motion. An oscillating mass on a spring or the motion of a simple pendulum are examples of objects in simple harmonic motion. When an object is in simple harmonic motion, the restoring force is directly proportional to the displacement and will act in opposition to that displacement, allowing the object to oscillate back and forth.

Objective

Exploration

A bungee jumper leaps from a tall structure and falls toward the ground. The bungee cord begins to stretch and transfers the kinetic energy of the fall into elastic potential energy, slowing the jumper to a stop.The cord then pulls him/her back up as the elastic potential energy turns back into kinetic energy. The jumper then oscillates up and down until their energy is completely dissipated.

Objective