Section III, 1921 [85] Trans. R.S.C. 



A New Vibration Experiment — Cylinders and Rods Balanced 

 on Cylinders 



By John Satterly, F. R.S.C. 



(Read May Meeting, 1921) 



At the close of the conference held in the Department of Physics 

 of the University of Toronto in January last, a distinguished chemist 

 and physicist, after looking over the mechanics section of the labora- 

 tory and examining the different experiments on vibration, suggested 

 the following experiment as an interesting exercise for the higher 

 students. 



I have, therefore, set it up and the following note gives the work 

 that has been done upon it. 



The experiment consists in balancing a cylinder at right angles 

 across another cylinder, setting it in up-and-down vibration like a 

 see-saw and finding its time of swing. By using different cylinders 

 a study mdy be made of the conditions of stability and the factors 

 upon which the time of swing depends. 



The figure gives an elevation of the two cylinders looked at in 

 the direction of the axis of the fixed cylinder. MN shows a portion 

 of the balanced cylinder in its horizontal position and MiNi shows it 

 when the cylinder is tilted. 



Let be the centre of the cross-section of the fixed cylinder, G 

 the position of the centre of gravity of the balanced cylinder when in 

 the horizontal position, d the position of the centre of gravity when 

 the balanced cylinder im depressed on one side to make a small angle 6 

 with the horizontal. 



To get the position of Gi let A and B be the points of contact 

 between the cylinders in the two positions. Measure off BAi equal 

 to the arc BA and draw A^d at right angles to and meeting the axis 

 of the cylinder in d. 



Join OAG. Draw OB to meet the axis of the balancing cylinder 

 in C. Join CGj. Draw a vertical line BD through B, a vertical line 

 GiE through Gi, and a horizontal line CDE to cut these verticals in 

 D and E respectively. Draw BF at right angles to OA. 



Let a = radius of cross-section of fixed cylinder. 



Let m, I, è = mass, length and radius of balancing cylinder. 



