# Understanding the Motion of a Harmonic Oscillator

This material is replicated on a number of sites as part of the SERC Pedagogic Service Project

#### Summary

In this interactive lecture demonstration students are guided to a full conceptual understanding of harmonic motion through the use of a variety of resources. This lecture and collection of demonstrations and simulations are intended for introducing the concepts of wave frequency, amplitude and period. More advanced students can also investigate the relationship between uniform circular motion and harmonic motion.

## Learning Goals

At the end of this activity the students will understand the relationship between sinusoidal waves and periodic oscillators. Specifically, they will be able to relate the

Amplitude of the wave and the oscillator

Period of the wave and the oscillator

Frequency of the wave and the oscillator

Velocity of the wave with the wavelength and frequency

More advanced students can extend this lesson to relate harmonic motion with circular motion.

Amplitude of the wave and the oscillator

Period of the wave and the oscillator

Frequency of the wave and the oscillator

Velocity of the wave with the wavelength and frequency

More advanced students can extend this lesson to relate harmonic motion with circular motion.

## Context for Use

This interactive lecture demonstration is intended for a high school class or small college class. It can be adapted for larger classes.

Equipment required:

2 students, a cart, a board, and a mass on a spring

A computer, motion detector and software and projection system

Equipment required:

2 students, a cart, a board, and a mass on a spring

A computer, motion detector and software and projection system

## Description and Teaching Materials

The demonstration for the first part of the lecture is a student being pushed on a cart across the room while recording the motion of a mass on a spring. A sinusoidal wave is produced and used to develop the vocabulary and concepts of wave motion. Specifics can be found here.

For the second part of the lecture a motion detector is placed underneath the mass on a spring and the motion is recorded and analyzed

For more advanced students, continue with an applet http://www.phys.hawaii.edu/~teb/java/ntnujava/shm/shm.html which shows the relationship between circular motion and harmonic motion, discussing angular frequency. Student worksheet for Understanding SHM (Microsoft Word 162bytes Jul3 08) Teacher/key for Understanding SHM (Acrobat (PDF) 162bytes Jul3 08)

For the second part of the lecture a motion detector is placed underneath the mass on a spring and the motion is recorded and analyzed

For more advanced students, continue with an applet http://www.phys.hawaii.edu/~teb/java/ntnujava/shm/shm.html which shows the relationship between circular motion and harmonic motion, discussing angular frequency. Student worksheet for Understanding SHM (Microsoft Word 162bytes Jul3 08) Teacher/key for Understanding SHM (Acrobat (PDF) 162bytes Jul3 08)

## Teaching Notes and Tips

This interactive demonstration will probably take at least 80 minutes of class time.

## Assessment

The teacher could take up the final graphs or circulate the room to insure they are correct on every paper.