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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. (b) If the mass in Fig. (a) and the two masses

Q. 14.13 (b) Figure 14.26 (a) shows a spring of force constant k clamped rigidly at one end and a mass m attached to its free end. force applied at the free end stretches the spring. Figure 14.26 (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. 14.26 (b) is stretched by the same force . (b) If the mass in Fig. (a) and the two masses in Fig. (b) are released, what is the period of oscillation in each case?

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(b).(a) In Fig, (a) we have

F=-kx

ma=-kx

(b) In fig (b) the two equal masses will be executing SHM about their centre of mass. The time  period of the system would be equal to a single object of same mass m attached to a spring of half the length of the given spring (or undergoing half the extension of the given spring while applied with the same force)

Spring constant of such a spring would be 2k

F=-2kx

ma=-2kx

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