Stiffness constant of a string (diagram included)
So I need to find the stiffness constant, (call it s) of this string.
As shown in the diagram, a mass m is at the centre of a light string of length 2L, fixed at both ends under a constant tension T. The mass oscillates in the plane of the page when released. It is displaced from the equilibrium position by x.
I know that the restoring force F= -sx.
I know that stiffness s is equal to the restoring force per unit displacement.
I need to find that the stiffness constant is equal to 2T/L.
I've already found that the total vertical force is 2T*sin(θ) downwards, and the horizontal forces cancel each other out which seems correct.
But how do I find the length of that displacement x?
EDIT: I'm taking θ to be the angle at the leftmost and rightmost corners of the diagram.
As shown in the diagram, a mass m is at the centre of a light string of length 2L, fixed at both ends under a constant tension T. The mass oscillates in the plane of the page when released. It is displaced from the equilibrium position by x.
I know that the restoring force F= -sx.
I know that stiffness s is equal to the restoring force per unit displacement.
I need to find that the stiffness constant is equal to 2T/L.
I've already found that the total vertical force is 2T*sin(θ) downwards, and the horizontal forces cancel each other out which seems correct.
But how do I find the length of that displacement x?
EDIT: I'm taking θ to be the angle at the leftmost and rightmost corners of the diagram.
(edited 10 years ago)
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