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    I really don't understand Simple Harmonic Motion when there are two elastic strings. I've looked at it, and I really don't understand...

    For example, this question;

    Particle mass 0.2kg, connected by two light elastic strings, each natural length 0.5m, modulus of elasticity 5N, and connected to points A and B on a smooth horizontal table. Midpoint of AB is O, and AB is 1m. The particle is displaced 0.3m towards B, to Point C and released from rest. Show that after t seconds, the displacement from O being x metres, that d^2x/dt^2 = -100x.

    I have no idea where to begin, and so as much help as possible would be greatly appreciated.
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    The force acting on the particle is only due to the string in tension. This force, from basic elasticity stuff:

    F=kx=\frac{\lambda x}{\ell}

    Also, a=\frac{d^2x}{dt^2}=\frac{F}{m}

    Using this, acceleration can be calculated in terms of displacement.

    EDIT: That said, I don't seem to be able to get the answer. Hmm...

    EDIT again: I seem to be able to get the answer if I treat the strings and springs, that can be compressed, however, by doubling the force up.
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    (Original post by sean712)
    I really don't understand Simple Harmonic Motion when there are two elastic strings. I've looked at it, and I really don't understand...

    For example, this question;

    Particle mass 0.2kg, connected by two light elastic strings, each natural length 0.5m, modulus of elasticity 5N, and connected to points A and B on a smooth horizontal table. Midpoint of AB is O, and AB is 1m. The particle is displaced 0.3m towards B, to Point C and released from rest. Show that after t seconds, the displacement from O being x metres, that d^2x/dt^2 = -100x.

    I have no idea where to begin, and so as much help as possible would be greatly appreciated.
    Are you sure they weren't springs?
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    Oh Yeah, sorry, they are springs :/

    So how did you get the answer? I've tried it and keep getting confused and ended up with a=-30 and no where near the answer...

    EDIT: I understand now! Thank you for your help
 
 
 
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Updated: March 27, 2011
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