Episode 300: Preparation for simple harmonic motion topic

Advance warning

This topic has many mathematical aspects. However, you will also want your students to gain a feel for the characteristics of simple harmonic motion. To this end, it will be useful if you can set up some large, slow oscillators, such as:

• a very long pendulum
• a mass on a long vertical spring
• a trolley or other mass tethered horizontally between springs

In addition, it will be useful if you can use an oscilloscope connected to a slow signal generator (frequency 1 Hz) to show a spot moving with SHM.

You can find a video clip and pictures of the Tacoma Narrows Bridge disaster on the University of Bristol website.

Main aims of this topic

Simple harmonic motion

Students will:

• recognise the characteristics of SHM
• state the condition required for SHM
• use equations and graphs which represent the variation of displacement, velocity and acceleration with time
• investigate mass-spring systems and the simple pendulum
• discuss the effects of damping on SHM
• describe changes to the ways energy is stored during SHM
• state the conditions required for resonance to occur, and its effects

Prior knowledge

This topic draws on several areas of mechanics which students are likely to have covered previously. You can use this topic to reinforce understanding of the following points:

• basic linear dynamics especially Newton’s Second Law in the form F = m × a
• Hooke’s Law
• resolving to find components of vectors
• graphs of sin( θ ) and cos( θ )
• circular measure (radians)
• motion in a circle (angular velocity ω , centripetal acceleration α (v²r )
• if students are not already familiar with small angle approximations, you can use this topic to introduce them (sin( θ )~ θ , cos( θ ) ~ 1 for small θ ; θ in radians).

Where this leads

This topic leads naturally into the topic of waves. Sinusoidal waveforms arise from sources executing SHM; in addition, the equations for SHM are similar to those for wave motion.