Answer:
 By calculation, it can be shown that;
 K =  
 
Whereby for constant K, as   increases,  x also increases.
 increases,  x also increases.
Explanation:
The experiment set up consisted of the use of a spring force to maintain the object in  circular path. 
The energy in the spring is given by
 .
. 
Rotational kinetic energy =  ·I·ω²
·I·ω²
Inertia,  I =   ·m·r²
·m·r²
ω = 
Substituting gives
Rotational kinetic energy =   ·
· 
=   ·m· v²
·m· v²
Equating both equations gives
K =  =
  =  
   
Within the proportionality limit, x ∝ r
therefore we can write x = c·r which gives
 =
 =  
 
Since  = angular acceleration, α, then
 = angular acceleration, α, then 
m×  = Angular force
 = Angular force
Therefore K = 
Therefore as Force, F increases, x also increases and the size of a spring force should be proportional to the amount of stretch in the spring.