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Why is time period not dependent on g for a mass spring system Watch

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    T = 2pi (m/k)^1/2 and k = tension/extension and tension is dependent on g so why is time period indepent of g?
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    (Original post by G.Y)
    T = 2pi (m/k)^1/2 and k = tension/extension and tension is dependent on g so why is time period indepent of g?
    Symmetry, the additional acceleration going down exactly cancels the additional deceleration going back up.
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    (Original post by natninja)
    Symmetry, the additional acceleration going down exactly cancels the additional deceleration going back up.
    So the a in a = -(2pi/T)^2x will always equal -g?
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    The reason is simple.
    Just as you rightly said,

    T = 2pi root(m/k)

    However, for a particular string or spring, the value of k is a constant.
    Hence, in contrast to what you think, k is not dependent on g

    Well, of course, k = Tension / Extension

    However, it is because k must remain constant, that we then agree that Tension is directly proportional to the extension.

    When g increases, Tension increases, so, the Extension also increases. k must stay constant.

    Hence, T does not depend on g.

    This is different in the case of mass m.
    When m increases, yes tension goes up, extension goes up so that k stays constant. But because the equation feeds on the value of m, T will have to increase with m.


    We can say the same for length in T = 2pi root (L/g)
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    (Original post by Onlineslayer)
    The reason is simple.
    Just as you rightly said,

    T = 2pi root(m/k)

    However, for a particular string or spring, the value of k is a constant.
    Hence, in contrast to what you think, k is not dependent on g

    Well, of course, k = Tension / Extension

    However, it is because k must remain constant, that we then agree that Tension is directly proportional to the extension.

    When g increases, Tension increases, so, the Extension also increases. k must stay constant.

    Hence, T does not depend on g.

    This is different in the case of mass m.
    When m increases, yes tension goes up, extension goes up so that k stays constant. But because the equation feeds on the value of m, T will have to increase with m.


    We can say the same for length in T = 2pi root (L/g)
    Thank you so much, I've understood now
 
 
 
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