A block of inertia \(m\) is attached to a light string wound around a uniform disk also of inertia \(m\) (Figure P11.74). The disk has radius \(R\) and rotates on a fixed horizontal axle through its center. The opposite side of the block is attached to a spring of force constant \(k\) and relaxed length \(\ell\) attached at the bottom of an inclined surface that makes an angle \(\theta\) with the horizontal. The block is at rest with the spring stretched a distance \(d\) from its relaxed length, with the block held in this position by a clamp. When the clamp is loosened so that the block is free to move, the block is pulled down the plane by the spring. What is the speed of the block when the spring is at half of its relaxed length? Ignore friction.

Data from Figure P11.74

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