202 Mr. Mallet on the Physical Conditions 



The equation for maximum extension may be put in a more convenient 

 form, for k- being = ^ if we call H the height -~ due to T^, it becomes, 



/" = l' + Jfr- + 2gH -\ = l' + y[l'{l' + 2R)l (34) 



which shows that I" exceeds I', the static extension or compression due to Phy 

 a mean proportional between I' and I' + 2H. This, therefore, measures the 

 effect due to the initial velocity of the straining load. 



If r = the semi-amplitude of oscillation, or 2r the amplitude, 



r = ](l'^^l) (35) 



If then T' be the time corresponding to \[l''+ ~hr)~^'^ ^^^ 7 the time 

 when the end of the bar has reached any extension or compression /, 



;==^'-rcosin A;(r-|-T'), (36) 



and the velocity at the corresponding point 



V= k y[r'- - (r - If] = kr sin k{T- T% (37) 



tiie value of the corresponding effort of the straining force being 



PI 



P'^Y- (38) 



Lastly, the time of one complete oscillation, 



and the number of oscillations per second, 



From what has been stated it is obvious that if, in place of the straining load 

 having an initial velocity, we have an elastic bar strained with a static load, and 



