A small mass m , attached to one end of a spring with a negligible mass and an unstretched length L , executes virtual oscillation with angular frequency ω 0 . When the mass is rotated with an angul

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A small mass m , attached to one end of a spring with a negligible mass and an unstretched length L , executes virtual oscillation with angular frequency ω 0 ​ . When the mass is rotated with an angular speed ω by holding the other end of the spring at a fixed point, the mass moves uniformly in a circular path in a horizontal plane. Then the increase in length of the spring during the rotation is

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The given situation can be shown as From figure, K ( x sin θ = m ω 2 ( L + x ) sin θ ⇒ K x = m ω 2 ( L + x ) ...(i) Also, m K ​ ​ = ω 0 ​ ⇒ K = m ω 0 2 ​ Substituting the value in Eq. (i) m ω 0 2 ​ x ⇒ x ​ = m ω 2 ( L + x ) = ω 0 2 ​ − ω 2 ω 2 L ​ ​

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