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

1. T = 2pi (m/k)^1/2 and k = tension/extension and tension is dependent on g so why is time period indepent of g?
2. (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.
3. (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?
4. 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)
5. (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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Updated: October 31, 2017
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