# S.H.M. with a cantilever

Practical Activity for 14-16

**Class practical**

This experiment could extend (or replace) the traditional pendulum or mass-on-a-spring experiments illustrating S.H.M.

Apparatus and Materials

- Metre rules
- G-clamps
- Slotted masses (100 g each)
- Sellotape
- Stopwatches
- Small, rough wooden blocks

Health & Safety and Technical Notes

It might be best advised to wear goggles in case something snaps.

Don't stand with toes underneath the slotted masses.

Read our standard health & safety guidance

Procedure

- G-clamp the metre rule securely to the bench using the wooden blocks to protect the rule and bench.
- Sellotape one or more slotted masses near the end of the rule.
- Twang and time several oscillations.
- Adjust the vibrating length (or mass attached) and repeat.

Teaching Notes

- You could use this experiment as a follow-up to the standard "g from a pendulum". There are more variables to play with so you can easily set up differentiated tasks for your students.
- In this case we can find
*E*for wood because for this cantilever we have ...
ω *x*= width of ruler*y*= thickness of ruler (scale to undersurface)*M*= mass Sellotaped on*L*= vibrating length*E*= Young modulus of wood*ω*= 2π/T- So T
^{2}v*M*(or*L*^{ 3}) gives you*E*from the gradient. - With a wide range of abilities you can have one group simply verifying it's S.H.M. (by proving -
*T*is independent of amplitude), another determining*E*, and another using log graphs to discover that*T*is proportional to -*L*^{3/2}. It's also a good one for error analysis; which term contributes the largest error in*E*(answers on a postcard)? - The vibrations are quite fast (especially at short lengths). To obtain an accurate result for
*T*, time many oscillations and find the average time for a single oscillation. - If you have the materials you can try things other than metre rules.

^{2}=

Exy

^{3}/ 4

*ML*

^{3}where

*Thank you to Wayne Morton for pointing out that there was an error in the formula that we previously printed.*

*This experiment was submitted by Jason Welch who is Head of Physics at County High School, Leftwich, Cheshire.*