and y^^o I C2_ c2 (^S) 



124 PERIOD OF VIBRATION OF STEAM VESSELS. 



If OB is called S, then 



It will be seen, therefore, that the component parallel to a diameter, of the ve- 

 locity of a point which travels with uniform velocity in a circular path, bears the 

 same relation to the velocity of the point that the velocity of the simple pendulum 

 at any point of its swing bears to the maximum velocity of the pendulum. If, then, 

 the pendulum swings through such a small arc that the chord and arc may be con- 

 sidered identical, the time taken to swing through arc Si will be the same as it takes 

 the point in Fig. 2 to move through a quadrant of radius Sij or 



2 2 71 1/ 



The time required for a double swing, or from A back to A again will be 



V7 27t _ 



In this case, where the weight is considered concentrated at a point, the expres- 

 sion J-^ of equation (i) is replaced by \/i, the length of the simple pendulum. 



COMPOUND PENDULUM. 

 Fig. 3, Plate 59. 



If the weight be not concentrated at a point as in the case of a simple pendu- 

 lum, but the pendulum consists of a bar of length L and unit weight of w pounds 

 (Fig. 3, Plate 59), the work done in swinging from ^ to O will be zvLyi, where 3/1 is 

 the height of the center of gravity of the bar above its lowest point. The kinetic 

 energy of the bar as it passes the vertical, will be — 



where a is the angular velocity. 



Equating work and kinetic energy, we have — 



wLy, = wL X — X — 

 3 2^ 



— It 





