Monday 18 June 2018

Pine tree cantilever oscillations

I watched the pine tree in the centre right of photo oscillating freely after being driven by the wind. I timed 6 oscillations in 27 seconds, so time period was 4.5 seconds. I looked for an equation and found one here
https://physics.stackexchange.com/questions/171198/derive-equation-for-a-cantilever-in-shm
Time period = 6.19*L^2/d x sqrt(density/Young Modulus). I looked up density of pine (510 kg per cubic metre) and Young Modulus of pine (9GPa). I d is the width of a rectangular cross-section. I used diameter instead which I estimated at 0.15m, though it is not uniform. I get a length of 21m. I think that's probably a bit big but not by much!