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# Figure 14.26 shows a spring of force constant k clamped rigidly at one end and a mass m attached to its free end. A force F applied at the free end stretches the spring. (a) What is the maximum extension

Q. 14.13 (a) Figure 14.30

(a) shows a spring of force constant k clamped rigidly at one end and a mass m attached to its free end. $A$ force $F$ applied at the free end stretches the spring. Figure 14.30 (b) shows the same spring with both ends free and attached to a mass m at either end. Each end of the spring in Fig. 14.30

(b) is stretched by the same force F.

(a) What is the maximum extension of the spring in the two cases?

Views

(a) Let us assume the maximum extension produced in the spring is x.

At maximum extension

$\\F=Kx\\ x=\frac{F}{k}$

(b) Let us assume the maximum extension produced in the spring is x. That is x/2 due to force towards left and x/2 due to force towards right

$\\F=k\frac{x}{2}+k\frac{x}{2}\\\Rightarrow x=\frac{F}{k}$

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