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# M3 elastic springs and strings question(2) watch

1. A light elastic string has natural length L and modulus (lamba). One end is fixed to a point A on a ceiling and a particle P of mass m is attached to the other end. P is held vertically below A so that AP=2L and then released. P has speed v when the extension of the string is x. Show that, while the string remains taut,

1/2mv^2 = L/2 ( (lamba) - 2mg ) + mgx - (lambda)x^2 / 2L

I have completed that part

I am stuck with this part:

By considering the speed of P when x=0 show that the string will never become slack provided 2mg > (lamba)
2. Certainly don't need to make two threads on this!
3. This is another question- I also posted this after the first question had been answered in the first thread, but then, it would be more easliy accessed here.

Could you help me with it please?

Thank you
4. Been a while since I looked at mechanics, it has become rusty, sorry!

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Updated: April 5, 2011
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