A light string has its two ends fastened together to form a loop of natural length "2l" and modulus of elasticity mg. The string is placed over two smooth fixed pegs A and B where AB is horizontal and of length 2l. A particle P of mass 2m is attached to the mid-point of the lower part of the loop and hangs in equilibrium vertically below C, the mid-point of AB.

d)Find the period of the motion.

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a) Explain why the extension of the string is equal to twice the length of AP.
b) Show that the distance CP is l.
P is projected vertically downwards from its equilibrium position.
c) Show that, providing the string does not break and P does not reach the level of AB, the subsequent motion is simple harmonic.

a), b), c) worked out but my period {d)} is $\displaystyle 4\pi \sqrt \frac{l}{g}$ while book's answer is $\displaystyle 2\pi \sqrt \frac{l}{g}$. I took, in the formula, mass as 2m and original length as 2l, as given question, but the answer disagrees. Anybody with a suggestion why this might be? :S :help: