# 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**

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 energy changes 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*=*ma* - 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 w,centripetal acceleration
*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). See the question 1 in the link below

Episode 225-1: Radians and angular speed (Word, 43 KB)

**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.

**Download this episode**

Episode 300: Preparation for simple harmonic motion topic (Word, 40 KB)