[satterly] 



THE PENDULUM 



29 



Plot a curve between the numbers in the first and fourth columns 

 and from the slope find the average value of the ratio force / displace- 

 ment. Compare this value with the average of the number in the last 

 column. Denote this constant by k. 



Here is a sample set of figures: 



Average 



85 



Therefore force (in dynes)=85 x displacement (in feet). 



Further Theory. — When the displacement of a body from its 

 position of rest is proportional to the displacing force, say k times 

 this force, it follows that the force urging it back towards its normal 

 position is also k times the displacement. Also when the body is 

 vibrating in the line of this displacement the product "mass of body 

 X its acceleration" is k times the displacement. But if the accelera- 

 tion is proportional to the displacement the motion of the body is 

 simple harmonic and the period is given by: 



In 



t = 2it 



displacement 

 acceleration 



, which may be written 



mass of body x displacement 

 mass of body x acceleration 



