Physics Graphs: Springs 
A spring is suspended from a rod and a mass is then attached. The length of the spring is measured at two positions: its original unstretched, equilibrium position (A) and its final stretched position (B). After calculating how far the spring was displaced from equilibrium at position B, a graph was plotted showing these two positions.
Original A

Stretched B

Distorting Force vs. Displacement




As more and more mass was placed on the spring, it was discovered that the spring no longer stretched linearly. In fact, the spring ceased to recover and remained permanently distorted (point C). This event is illustrated in the broken region shown in the following graph.



General Questions 



Calculate the spring constant (k) using the following data:
position


stretch


A

10 cm

0

0

B

14 cm

4 cm

10 N


If instead, a mass weighing 8 N (m = 0.816 kg) had been suspended from the spring, how far would the spring have stretched? 
What would you estimate the length of the spring to be if a 20N mass were to be suspended? 
At position B, the same spring is then put into oscillation and the following graph of position vs time was recorded. X_{o} represents the amplitude of the spring about position B.
The formula for the time required for one vibration, or the period (T), of an oscillating spring is:
Using the information about point B and the value of spring constant calculated earlier, calculate the period of the spring. 
According to the diagram, how many vibrations did the spring make? 
For how many seconds was the spring's oscillations recorded? 




C Colwell


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