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Question

Figure (a) shows a spring of force constant k fixed at one end and carrying a mass m at the other end placed on a horizontal frictionless surface. The spring is stretched by a force F. Figure (b) shows the same spring with both ends free and a mass m fixed at each free end. Each of the spring is stretched by the same force F. The masses in both the cases, a and b are released. Find the maximum extension of the spring in both cases.
784538_53829533661e4c19b4c8b8ad6ca61984.PNG

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Solution

For figure I(A), Tension T=kx
T=F
From the figure I(B),
At time of maximum streach or maximum tension both block move with equal acceleration
F=(m+m)a
a=F2m
By law of motion,
FT=ma
FT=m×F2m
T=F2

1006131_784538_ans_597e228f88044145994016e050ef9d65.png

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