A particle of mass km is placed on top of a light, vertical spring of natural length

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A particle of mass km is placed on top of a light, vertical spring of natural length 2a. The modulus of elasticity of the spring is 3mg and the spring is standing upright so that it lies in a vertical plane.

a. Find the compression in the spring in terms of k and a.

b. Find the value of k such that the length of the spring is halved due to the weight of the particle.

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