A small circus dog walks on a rolling solid cylinder. The dog remains at a fixed height above the ground corresponding to the angle \(\theta= 30^{\circ}\). If the mass of the cylinder is 4 times larger than the mass of the dog, find the acceleration \(a\) of the cylinder's center of mass **in m/s\(^2\)**. Assume that the cylinder rolls without slipping.

**Details and assumptions**

- The acceleration of gravity is \(-9.8~\mbox{m/s}^2\).

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