## Episode 300: Preparation for simple harmonic motion topic

Teaching Guidance for 16-19

- Level Advanced

#### 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

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*(*v*^{ 2}*r*) - 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.