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.

Answer 1

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

$F=(m+m)a$

$a=\frac{F}{2m}$

By law of motion,

$F-T=ma$

$F-T=m\times \frac{F}{2m}$

$T=\frac{F}{2}$