One end of a spring of natural length \( \ell \) and spring constant \( k \) is fixed at the gro...

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One end of a spring of natural length \( \ell \) and spring constant \( k \) is fixed at the ground and the other is fitted with a smooth ring of mass \( \mathrm{m} \) which is allowed to slide on a horizontal rod fixed at a height \( \ell \) (figure). Initially, the spring makes an angle of \( \theta \) with the vertical when the system is released from rest. If the speed of the ring when the spring becomes vertical is \( (2 \ell / 3) \sqrt{\frac{k}{m}} \mathrm{~m} / \mathrm{s} \) then find the value of angle \( \theta \) (in degree):
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