1915-16.] Torsional Vibration of Beams of Commercial Section. 35 
ment and the other symbols have the significance already ascribed to 
them. 
When the system is vibrating, at the point of maximum angular dis- 
placement, the whole of the energy is in the form of potential energy and 
the restoring moment is given by the relationship 
but 
T 
Restoring moment = — (0 X + 0) - wr ; 
and from (3) 
T = wr, 
T = CJ 
e~ l * 
CJ 
. \ Restoring moment = — 0. 
Also, it may be shown that the displacing moment 
' df 
where I is the mass moment of inertia of the load about the axis 00. 
Since the sum total of the energy throughout a complete vibration 
varies in kind but not in amount, the kinetic energy of the system as it 
passes through its mean position must equal the potential energy of the 
system at the point of extreme angular displacement. Hence 
-rddO CJ, 
( 4 ) 
