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``elastic string question'' by curious on 2009-03-25 07:15:12
The ends of a light elastic string, of natural length 2L and modulus of elasticity X are attached to fixed points A and B, where AB is horizontal and AB = 3L. A particle P of mass m, is attached to the mid-point of the string. The particle is held at rest with the string horizontal and is then released. In the subsequent motion air resistance may be neglected.
The particle falls a distance 2L before first coming instantaneously to rest.

Show that X = mg.

(Note: I know that the particle will oscillate in SHM, but I was unable to prove the relation X = mg. Please show step by step.
The question is taken from Edexcel Mechanics M2 June 1997 question 7. If you have the mark scheme also, please send.)

Thanks
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